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A thermodynamically consistent diffuse interface model for multicomponent twophase flow with partial miscibility Comput. Math. Appl. (IF 2.9) Pub Date : 20230925
Chunhua Zhang, Zhaoli Guo, LianPing WangIn this paper, we aim to develop a thermodynamically consistent diffuse interface model for twophase multicomponent fluids with partial miscibility based on the second law of thermodynamics. The resulting governing equations consist of the AllenCahn equation for the order parameter representing the phase volume fraction, the CahnHilliard equation for the molar fraction of each component in the mixture

Convergence of a simple discretization of the finite Hilbert transformation Comput. Math. Appl. (IF 2.9) Pub Date : 20230920
Martin CostabelFor a singular integral equation on an interval of the real line, we study the behavior of the error of a deltadelta discretization. We show that the convergence is nonuniform, between order O(h2) in the interior of the interval and a boundary layer where the consistency error does not tend to zero.

Hybrid fifthorder unequalsized weighted essentially nonoscillatory scheme for shallow water equations Comput. Math. Appl. (IF 2.9) Pub Date : 20230918
Zhenming Wang, Jun Zhu, Linlin Tian, Ning ZhaoIn this paper, we propose a new discontinuous sensor and a finite difference hybrid unequalsized weighted essentially nonoscillatory (WENO) scheme with fifthorder accuracy for solving shallow water equations with or without source terms. The developed discontinuous sensor is directly designed based on the highest degree polynomial obtained from the fivepoint stencil in the unequalsized WENO procedures

A twostage deep learning architecture for model reduction of parametric timedependent problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230914
Isabella Carla Gonnella, Martin W. Hess, Giovanni Stabile, Gianluigi RozzaParametric timedependent systems are of a crucial importance in modeling real phenomena, often characterized by nonlinear behaviours too. Those solutions are typically difficult to generalize in a sufficiently wide parameter space while counting on limited computational resources available. As such, we present a general twostage deep learning framework able to perform that generalization with low

The infsup constant for hpCrouzeixRaviart triangular elements Comput. Math. Appl. (IF 2.9) Pub Date : 20230910
Stefan SauterIn this paper, we consider the discretization of the twodimensional stationary Stokes equation by CrouzeixRaviart elements for the velocity of polynomial order k≥1 on conforming triangulations and discontinuous pressure approximations of order k−1. We will bound the infsup constant from below independent of the mesh size and show that it depends only logarithmically on k. Our assumptions on the

A time multiscale decomposition in cyclic elastoplasticity Comput. Math. Appl. (IF 2.9) Pub Date : 20230910
Angelo Pasquale, Sebastian Rodriguez, Khanh Nguyen, Amine Ammar, Francisco ChinestaFor the numerical simulation of timedependent problems, recent works suggest the use of a time marching scheme based on a tensorial decomposition of the time axis. This timeseparated representation is straightforwardly introduced in the framework of the Proper Generalized Decomposition (PGD). The time coordinate is transformed into a multidimensional time through new separated coordinates, the micro

Blending spline surfaces over polygon mesh and their application to isogeometric analysis Comput. Math. Appl. (IF 2.9) Pub Date : 20230911
Tatiana KravetcFinite elements are allowed to be of a shape suitable for the specific problem. This choice defines thereafter the accuracy of the approximated solution. Moreover, flexible element shapes allow for the construction of an arbitrary domain topology. Polygon meshes are a common representation of the domain that cover any choice of the finite element shape. Being an alternative tool for modeling and analysis

The analogue of graddiv stabilization in DG method for a coupled Stokes and Darcy problem Comput. Math. Appl. (IF 2.9) Pub Date : 20230912
Jing Wen, Zhangxing Chen, Yinnian HeMany stable and convergent numerical methods are not pressure robust for an incompressible flow problem, due to the relaxation of a discrete divergence constraint called poor mass conservation. As a result, the velocity error is polluted by the pressure error, particularly when the fluid viscosity is relatively small and pressure is comparably large. A graddiv stabilization is an efficient remedy

Symmetric fractional order reduction method with L1 scheme on graded mesh for time fractional nonlocal diffusionwave equation of Kirchhoff type Comput. Math. Appl. (IF 2.9) Pub Date : 20230914
Pari J. Kundaliya, Sudhakar ChaudharyIn this article, we propose a linearized fullydiscrete scheme for solving a time fractional nonlocal diffusionwave equation of Kirchhoff type. The scheme is established by using the finite element method in space and the L1 scheme in time. We derive the αrobust a priori bound and a priori error estimate for the fullydiscrete solution in L∞(H01(Ω)) norm, where α∈(1,2) is the order of time fractional

Simulation of the deformation for cycling chemomechanically coupled battery active particles with mechanical constraints Comput. Math. Appl. (IF 2.9) Pub Date : 20230914
R. Schoof, G.F. Castelli, W. DörflerNextgeneration lithiumion batteries with silicon anodes have positive characteristics due to higher energy densities compared to stateoftheart graphite anodes. However, the large volume expansion of silicon anodes can cause high mechanical stresses, especially if the battery active particle cannot expand freely. In this article, a thermodynamically consistent continuum model for coupling chemical

L∞ and L2norms superconvergence of the tetrahedral quadratic finite element Comput. Math. Appl. (IF 2.9) Pub Date : 20230910
Jinghong Liu, Qiyong Li, Zhiguang Xiong, Qiding ZhuConsider the quadratic finite element method over a regular family of uniform tetrahedral partitions for the threedimensional Poisson equation. Utilizing properties of the bubble function and estimates for discrete Green's function, we derive a pointwise superconvergent estimate for the finite element approximation in the sense of L∞norm. Furthermore, the L2norm superconvergent estimate is also

Improving the thirdorder WENO schemes by using exponential polynomial space with a locally optimized shape parameter Comput. Math. Appl. (IF 2.9) Pub Date : 20230906
Kyungrok Lee, JungIl Choi, Jungho YoonIn this study, we introduce a novel weighted essentially nonoscillatory (WENO) conservative finitedifference scheme that improves the performance of the known thirdorder WENO methods. To approximate sharp gradients and high oscillations more accurately, we incorporate an interpolation method using a set of exponential (or trigonometric) polynomials with an internal shape parameter. In particular

Numerical study of twodimensional Burgers' equation by using a continuous Galerkin method Comput. Math. Appl. (IF 2.9) Pub Date : 20230907
Zhihui Zhao, Hong LiIn this article, we use spacetime continuous Galerkin (STCG) method to find the numerical solution for twodimensional (2D) Burgers' equation. The STCG method differs from conventional finite element methods, both the spatial and temporal variables are discretized by finite element method, thus it can easily obtain the high order accuracy in both time and space directions and the corresponding discrete

Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression Comput. Math. Appl. (IF 2.9) Pub Date : 20230906
Ludovica Cicci, Stefania Fresca, Mengwu Guo, Andrea Manzoni, Paolo ZuninoUncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with inputoutput maps involving the solution of nonlinear differential problems, because of the need to query expensive numerical solvers repeatedly. Projectionbased reduced order models (ROMs), such as the Galerkinreduced basis (RB) method, have been

A diagonal finite elementprojectionproximal gradient algorithm for elliptic optimal control problem Comput. Math. Appl. (IF 2.9) Pub Date : 20230904
Jitong Lin, Xuesong Chen 
The nonconforming lockingfree virtual element method for the Biot's consolidation model in poroelasticity Comput. Math. Appl. (IF 2.9) Pub Date : 20230904
Hao Liang, Hongxing RuiIn this work, a lockingfree nonconforming virtual element method for the threefield Biot's model (the displacements, Darcy velocity and pore pressure) is developed and analyzed. We solve the model as: nonconforming VEM for the displacements, RTlike VEM for Darcy velocity and pressure. We show the wellposedness and the optimal error estimates of the discrete schemes. The numerical experiments support

Weak Galerkin finite element method for second order problems on curvilinear polytopal meshes with Lipschitz continuous edges or faces Comput. Math. Appl. (IF 2.9) Pub Date : 20230905
Qingguang Guan, Gillian Queisser, Wenju ZhaoIn this paper, we propose new basis functions defined on curved sides or faces of curvilinear elements (polygons or polyhedrons with curved sides or faces) for the weak Galerkin finite element method. Those basis functions are constructed by collecting linearly independent traces of polynomials on the curved sides/faces. We then analyze the modified weak Galerkin method for the elliptic equation and

A pollutionfree ultraweak FOSLS discretization of the Helmholtz equation Comput. Math. Appl. (IF 2.9) Pub Date : 20230901
Harald Monsuur, Rob StevensonWe consider an ultraweak first order system discretization of the Helmholtz equation. When employing the optimal test norm, the ‘ideal’ method yields the best approximation to the pair of the Helmholtz solution and its scaled gradient w.r.t. the norm on L2(Ω)×L2(Ω)d from the selected finite element trial space. On convex polygons, the ‘practical’, implementable method is shown to be pollutionfree

Output tracking for a 1D wave equation with velocity recirculation via boundary control Comput. Math. Appl. (IF 2.9) Pub Date : 20230831
Shuangxi Huang, FengFei JinIn this paper, we consider output tracking and disturbance rejection for a 1D wave equation with indomain feedback/recirculation of an intermediate point velocity. The performance output is an intermediate point displacement and the control matches the general disturbance. We first use the active disturbance rejection control method to design a disturbance estimator to estimate the disturbance. Then

L1robust analysis of a fourthorder blockcentered finite difference method for twodimensional variablecoefficient timefractional reactiondiffusion equations Comput. Math. Appl. (IF 2.9) Pub Date : 20230830
Li Ma, Hongfei Fu, Bingyin Zhang, Shusen XieIn this paper, we develop a highorder finite difference scheme for the twodimensional timefractional reactiondiffusion equation with variably diffusion coefficient, in which the nonuniform L1 time stepping method on graded mesh is utilized for temporal discretization to compensate for the possible temporal accuracy lost caused by the initial weak singularity, and by introducing a flux variable

A stabilizerfree weak Galerkin finite element method with Alikhanov formula on nonuniform mesh for a linear reactionsubdiffusion problem Comput. Math. Appl. (IF 2.9) Pub Date : 20230828
Jie Ma, Fuzheng Gao, Ning DuWe develop a temporally secondorder stabilizerfree weak Galerkin (SFWG) finite element method with unequal time steps for reactionsubdiffusion equation in multiple space dimensions. In consideration of initial singularity of the solution, we prove a sharp error estimate on nonuniform time steps by two tools: discrete fractional Grönwall inequality and error convolution structure analysis. Furthermore

Wellbalanced energystable residual distribution methods for the shallow water equations with varying bottom topography Comput. Math. Appl. (IF 2.9) Pub Date : 20230829
Wei Shyang Chang, Muna Mohammed Bazuhair, Farzad Ismail, Hossain Chizari, Mohammad Hafifi Hafiz IshakThis paper presents an alternative wellbalanced and energy stable method for the system of nonhomogeneous Shallow Water Equations (SWE) on unstructured grids based on the residual distribution (RD) approach. The motivation of the work is based on the grid insensitivity of RD method. The newly proposed method has a positive first order part, a linearitypreserving second order scheme as well as a

A bilateral preconditioning for an L2type allatonce system from timespace nonlocal evolution equations with a weakly singular kernel Comput. Math. Appl. (IF 2.9) Pub Date : 20230829
YongLiang Zhao, XianMing Gu, Hu LiIn this paper, we concentrate on design a bilateral preconditioning for allatonce system from multidimensional timespace nonlocal evolution equations with a weakly singular kernel. Firstly, we propose an implicit difference scheme for this equation by employing an L2type formula. Then, we prove the stability and the convergence of the proposed scheme. Based on such a numerical scheme, an L2type

An iterative decomposition coupling algorithm between TDFEM and TDBEM with independent spatial discretization on the interface Comput. Math. Appl. (IF 2.9) Pub Date : 20230825
Weidong Lei, Xiaofei Qin, Hongjun Li, Youhua FanIn order to make good use of the inherent advantages of the FEM and the BEM formulations, an iterative decomposition coupling algorithm between timedomain FEM and timedomain BEM with independent spatial discretization on the interface is proposed for elastodynamic problems. In the coupling process, based on the conditions of the displacement continuity and the force equilibrium on the interface,

Positivitypreserving nonstaggered central difference schemes solving the twolayer open channel flows Comput. Math. Appl. (IF 2.9) Pub Date : 20230825
Xu Qian, Jian DongThis paper aims to propose positivitypreserving nonstaggered central difference schemes solving the twolayer shallow water equations with a nonflat bottom topography and geometric channels. One key step is to discretize the bed slope source term and the nonconservative product term due to the exchange of the momentum based on defining auxiliary variables. The secondorder accuracy in space can be

A coefficient identification problem for a system of advectionreaction equations in water quality modeling Comput. Math. Appl. (IF 2.9) Pub Date : 20230824
Dinh Nho Hào, Nguyen Trung Thành, Nguyen Van Duc, Nguyen Van ThangA coefficient identification problem (CIP) for a system of onedimensional advectionreaction equations using boundary data is considered. The advectionreaction equations are used to describe the transportation of pollutants in rivers or streams. Stability for the considered CIP is proved using global Carleman estimates. The CIP is solved using the leastsquares approach accompanied with the adjoint

Optimal polynomial feedback laws for finite horizon control problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230824
Karl Kunisch, Donato VásquezVarasA learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by using the HamiltonJacobiBellman (HJB) equation. The convergence of the method is analyzed, while paying special attention to avoid the use of a global Lipschitz

A simplified lattice Boltzmann implementation of the quasistatic approximation in pipe flows under the presence of nonuniform magnetic fields Comput. Math. Appl. (IF 2.9) Pub Date : 20230822
H.S. Tavares, B. Magacho, L. Moriconi, J.B.R. LoureiroWe propose a singlestep simplified lattice Boltzmann algorithm capable of performing magnetohydrodynamic (MHD) flow simulations in pipes for very small values of magnetic Reynolds numbers Rm. In some previous works, most lattice Boltzmann simulations are performed with values of Rm close to the Reynolds numbers for flows in simplified rectangular geometries. One of the reasons is the limitation of

Efficient strategy for spacetime based finite element analysis of vibrating structures Comput. Math. Appl. (IF 2.9) Pub Date : 20230821
Bartłomiej Dyniewicz, Jacek M. Bajkowski, Czesław I. BajerThis paper presents an efficient parallel computing strategy to solve largescale structural vibration problems. The proposed approach utilises a novel direct method that operates using simplexshaped spacetime finite elements and allows for the direct decoupling of variables during the assembly of global matrices. The method uses consistent stiffness, inertia and damping matrices and deals with nonsymmetric

Scalable DPG multigrid solver for Helmholtz problems: A study on convergence Comput. Math. Appl. (IF 2.9) Pub Date : 20230821
Jacob Badger, Stefan Henneking, Socratis Petrides, Leszek DemkowiczThis paper presents a scalable multigrid preconditioner targeting largescale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of highfrequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from O(107) degrees of freedom (DOFs)

A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem Comput. Math. Appl. (IF 2.9) Pub Date : 20230818
WenHui Chu, ZhuoJia Fu, ZhuoChao Tang, WenZhi Xu, XiaoYing ZhuangIn the present work, we developed the Neural Networks (NNs) for identifying unknown surface shape of inner wall in the twodimensional pipeline based on the temperature at uniformly distributed measuring points. The steadystate governing equation is transformed into the anisotropic heat conduction equations, and the irregularly shaped inner boundary is identified by the estimation of circumferential

A modulus iteration method for nonnegatively constrained TV image restoration Comput. Math. Appl. (IF 2.9) Pub Date : 20230818
Jianjun Zhang, Xi ZhangIn this paper, we apply the ideas of modulus methods to the problem of nonnegatively constrained image restoration based on total variation (TV) regularization and present a modulus iteration method for this problem. The proposed method has the potential to effectively handle nonnegative constraint for image restoration. We prove the convergence of the proposed method. Experimental results show that

Tentpitcher spacetime discontinuous Galerkin method for onedimensional linear hyperbolic and parabolic PDEs Comput. Math. Appl. (IF 2.9) Pub Date : 20230816
Giang D. Huynh, Reza AbediWe present a spacetime DG method for 1D spatial domains and three linear hyperbolic, damped hyperbolic, and parabolic PDEs. The latter two correspond to MaxwellCattaneoVernotte (MCV) and Fourier heat conduction problems. The method is called the tentpitcher spacetime DG method (tpSDG) due to its resemblance to the causal spacetime DG method (cSDG) wherein the solution advances in time by pitching

Nonlinear disturbance observerbased robust predefined time tracking and vibration suppression control for the rigidflexible coupled robotic mechanisms with large beamdeformations Comput. Math. Appl. (IF 2.9) Pub Date : 20230814
Xingyu Zhou, Haoping Wang, Ke Wu, Yang Tian, Gang ZhengIn order to establish the dynamic equations of the rigidflexible coupled robotic mechanisms with large beamdeformations over the horizontal plane, a thorough modeling technique founded on the virtual work concept has been proposed. Based on the transformed fullactuated model, the predefinedtime robust sliding mode control strategy is developed to track the prescribed angular positions of the rigidflexible

Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient Comput. Math. Appl. (IF 2.9) Pub Date : 20230811
Haowei Liu, Zhiyong Liu, Qiuyan Xu, Jiye YangThe equilibrium radiation diffusion equation has been widely used in astrophysics, inertial confinement fusion and others. Since the simulation domain consists of many complicated domains and the material properties in each domain are different, the diffusion coefficient usually has a strong discontinuity at the interface. Because the equilibrium radiation diffusion equation is often built on complicated

On the convergence of a low order Lagrange finite element approach for natural convection problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230811
C. Legrand, F. Luddens, I. DanailaThe purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and temperature) is wellposed if used with a penalty term in the divergence equation, to compensate the loss of an infsup condition. With mild assumptions on the pressure

Legendretau Chebyshev collocation spectral element method for Maxwell's equations with material interfaces of two dimensional transverse magnetic mode Comput. Math. Appl. (IF 2.9) Pub Date : 20230810
Cuixia Niu, Heping Ma, Dong LiangIn this paper, a Legendretau Chebyshev collocation spectral element method is developed for solving Maxwell's equations with material interfaces in two dimensions. The transverse magnetic mode is considered mainly. The developed scheme treats the interface conditions in a way like the natural boundary condition based on a reasonable weak formulation, which makes the numerical solution retain the original

Weak Galerkin finite element methods for H(curl;Ω) and H(curl,div;Ω)elliptic problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230809
Raman Kumar, Bhupen DekaWeak Galerkin finite element methods (WGFEMs) for H(curl;Ω) and H(curl,div;Ω)elliptic problems are investigated in this paper. The WG method as applied to curlcurl and graddiv problems uses two operators: discrete weak curl and discrete weak divergence, with appropriately defined stabilizations that enforce a weak continuity of the approximating functions. This WG method is highly flexible by allowing

Plain convergence of goaloriented adaptive FEM Comput. Math. Appl. (IF 2.9) Pub Date : 20230807
Valentin Helml, Michael Innerberger, Dirk PraetoriusWe discuss goaloriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show plain convergence in a setting that relies only on structural

Energy stable schemes for the KleinGordonZakharov equations Comput. Math. Appl. (IF 2.9) Pub Date : 20230808
Jiaojiao Guo, Qingqu ZhuangBased on the traditional scalar auxiliary variable (SAV) method, the exponential SAV (ESAV) method, and the Lagrange multiplier method, three efficient energy stable schemes are proposed to solve the KleinGordonZakharov equations. All proposed schemes lead to linear equations with constant coefficients to be solved in each time step. The first two schemes are proved to preserve two different modified

IgABEM for 3D Helmholtz problems using conforming and nonconforming multipatch discretizations and Bspline tailored numerical integration Comput. Math. Appl. (IF 2.9) Pub Date : 20230808
Bruno Degli Esposti, Antonella Falini, Tadej Kanduč, Maria Lucia Sampoli, Alessandra SestiniAn Isogeometric Boundary Element Method (IgABEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth multipatch representation of their finite boundary surface. The discretization spaces are formed by C0 interpatch continuous functional spaces whose restriction to a patch simplifies to the span of tensor product Bsplines composed

An immersed weak Galerkin method for elliptic interface problems on polygonal meshes Comput. Math. Appl. (IF 2.9) Pub Date : 20230808
Hyeokjoo Park, Do Y. KwakIn this paper we present an immersed weak Galerkin method for solving secondorder elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on each edge and broken linear polynomials satisfying the interface conditions in each element. For triangular meshes, such broken linear polynomials coincide with the

Gradient viscoelastic virtual boundary for numerical simulation of wave propagation Comput. Math. Appl. (IF 2.9) Pub Date : 20230808
Techao Zhang, Xiaoshan Cao, Siyuan ChenA type of artificial boundary layer for the numerical simulation of wave propagation, which is named the gradient viscoelastic (GV) boundary layer, is proposed in this study. The setting of the GV boundary layer was established according to the propagation behavior of the longitudinal wave in the elastic GV rod, the analytical solution of the longitudinal wave propagation in the GV rod was obtained

A simple shape transformation method based on phasefield model Comput. Math. Appl. (IF 2.9) Pub Date : 20230804
Ziwei Han, Heming Xu, Jian WangIn this paper, we propose a simple and fast shape transformation method. This method is based on the AllenCahn (AC) partial differential equation and uses the edge stop function to constrain evolution. We use the operator splitting method to control the equation for splitting, and use the explicit Euler's method to solve the discrete equation. Based on the source shape and the target shape, our phasefield

A parallel finite element method based on fully overlapping domain decomposition for the steadystate Smagorinsky model Comput. Math. Appl. (IF 2.9) Pub Date : 20230803
Bo Zheng, Yueqiang ShangAn efficient parallel finite element method is introduced for solving the steadystate Smagorinsky model in which a fully overlapping domain decomposition is considered for parallelization. The crucial idea of the method is to utilize a locally refined multiscale mesh that is fine around its own subdomain and coarse elsewhere to calculate a local finite element solution. On the basis of an existing

Semi and fully discrete error analysis for elastodynamic interface problems using immersed finite element methods Comput. Math. Appl. (IF 2.9) Pub Date : 20230803
Yuan Chen, Songming Hou, Xu ZhangIn this paper, we present an immersed finite element (IFE) method for solving the elastodynamics interface problems on interfaceunfitted meshes. For spatial discretization, we use vectorvalued P1 and Q1 IFE spaces. We establish some important properties of these IFE spaces, such as inverse inequalities, which will be crucial in the error analysis. For temporal discretization, both the semidiscrete

A twolevel additive Schwarz preconditioner for the Nitsche extended finite element approximation of elliptic interface problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230803
Hanyu Chu, Ying Cai, Feng Wang, Jinru ChenIn this paper, we propose a twolevel additive Schwarz preconditioner for the Nitsche extended finite element discretization of elliptic interface problems. The intergrid transfer operators between the coarse mesh and the fine mesh spaces are constructed and a stable space decomposition is given. It is proved that the condition number of the preconditioned system is bounded by C(1+Hδ+Hh), where H and

Unsteady oblique stagnation point flow with improved pressure field and fractional Cattaneo–Christov model by finite differencespectral method Comput. Math. Appl. (IF 2.9) Pub Date : 20230802
Yu Bai, Xin Wang, Yan ZhangUnsteady oblique stagnation point flow, heat and mass transfer of generalized OldroydB fluid over an oscillating plate are investigated. The upperconverted derivative is introduced to the constitutive equation of fractional OldroydB fluid. The terms of pressure are inventively solved by means of the momentum equation far from the plate. Furthermore, fractional Cattaneo–Christov double diffusion

Robintype domain decomposition with stabilized mixed approximation for incompressible flow Comput. Math. Appl. (IF 2.9) Pub Date : 20230802
Yani Feng, Qifeng Liao, David SilvesterIn this paper we present a nonoverlapping Robintype multidomain decomposition method based on stabilized Q1–P0 mixed approximation (RMDDQ1P0) for incompressible flow problems. The global Stokes and NavierStokes equations are decomposed into a series of local problems through Robintype domain decomposition, and local problems are solved through the local jump stabilized Q1–P0 approximation. The

A continuous hpmesh model for discontinuous PetrovGalerkin finite element schemes with optimal test functions Comput. Math. Appl. (IF 2.9) Pub Date : 20230802
Ankit Chakraborty, Georg MayWe present an anisotropic hpmesh adaptation strategy using a continuous mesh model for discontinuous PetrovGalerkin (DPG) finite element schemes with optimal test functions, extending our previous work [1] on hadaptation. The proposed strategy utilizes the builtin residualbased error estimator of the DPG discretization to compute both the polynomial distribution and the anisotropy of the mesh

Simultaneous determination of the spacedependent source and initial value for a twodimensional heat conduction equation Comput. Math. Appl. (IF 2.9) Pub Date : 20230801
Yu Qiao, Xiangtuan XiongIn this article, we investigate an inverse and illposed problem to simultaneously reconstruct the spacedependent source and initial value associated with a twodimensional heat conduction equation based on the additional temperature data. An existence and uniqueness theorem is deduced by the contraction mapping principle. To obtain stable approximate solutions, we propose a fractional Landweber iteration

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives Comput. Math. Appl. (IF 2.9) Pub Date : 20230727
Andrew M. Jones, Peter A. Bosler, Paul A. Kuberry, Grady B. WrightApproximating differential operators defined on twodimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBFFD) have been shown to be effective for this task as they can give high orders of accuracy at low computational

Neural networks based on power method and inverse power method for solving linear eigenvalue problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230727
Qihong Yang, Yangtao Deng, Yu Yang, Qiaolin He, Shiquan ZhangIn this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential operator is realized by automatic differentiation. The eigenfunction of the eigenvalue problem is learned by the neural network and the iterative algorithms are implemented

Goaloriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and parabolic problems Comput. Math. Appl. (IF 2.9) Pub Date : 20230726
Emmanuel Creusé, Serge Nicaise, Zuqi TangWe present a unified framework for goaloriented estimates for elliptic and parabolic problems that combines the dualweighted residual method with equilibrated flux and potential reconstruction. These frameworks allow to analyze simultaneously different approximation schemes for the space discretization of the primal and the dual problems such as conforming or nonconforming finite element methods

A hybrid probabilistic domain decomposition algorithm suited for very largescale elliptic PDEs Comput. Math. Appl. (IF 2.9) Pub Date : 20230725
Francisco Bernal, Jorge MorónVidal, Juan A. AcebrónState of the art domain decomposition algorithms for largescale boundary value problems (with M≫1 degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers inherent to iterative linear algebra. Here, we introduce PDDSparse, a different approach to scientific supercomputing which relies on a “FeynmanKac formula for domain decomposition”

Spacetime adaptivity for a multiscale cancer invasion model Comput. Math. Appl. (IF 2.9) Pub Date : 20230725
V.S. Aswin, J. Manimaran, Nagaiah ChamakuriThe parallel spacetime adaptivity techniques for solving a cancer invasion model are investigated in the present work. Mathematically, the model comprises three coupled reactiondiffusion equations that characterize the cancer cell density evolution, the matrixdegrading enzymes and the extracellular matrix. The numerical realization demands fine resolutions both in spatial and temporal due to the

Limit equations of adaptive Erlangization and their application to environmental management Comput. Math. Appl. (IF 2.9) Pub Date : 20230724
Hidekazu Yoshioka, Tomomi Tanaka, Futoshi AranishiAdaptive Erlangization is a flexible observation/intervention strategy for system management based on randomized observation frequencies. The main contributions of this paper are the derivation and computation of some limit equation arising in the stochastic control under ambiguity along with its engineering application. In particular, with a focus on environmental management, we consider a novel longterm

A new gas kinetic BGK scheme based on the characteristic solution of the BGK model equation for viscous flows Comput. Math. Appl. (IF 2.9) Pub Date : 20230720
The gas kinetic BhatnagarGrossKrook (BGK) scheme proposed by Xu achieved great success and has been receiving a lot of attention during the past two decades. In this work, we proposed a new gas kinetic BhatnagarGrossKrook (BGK) scheme for viscous flows. The proposed gas kinetic scheme is derived from the characteristic solution rather than the formal integral solution of the BGK model equation

Nonrelaxed finite volume fractional step schemes for unsteady incompressible flows Comput. Math. Appl. (IF 2.9) Pub Date : 20230720
Despite their wellestablished efficiency and accuracy, fractionalstep schemes are not commonly used in finite volume methods. This article presents first, second, and thirdorder intime fractional step schemes to solve incompressible convective timedependent flows using collocated meshes. The fractional step methods are designed from a fully discrete problem and allow for optimal convergence

An accurate and robust Eulerian finite element method for partial differential equations on evolving surfaces Comput. Math. Appl. (IF 2.9) Pub Date : 20230720
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard spacetime finite element spaces on a fixed bulk mesh to the spacetime surface. The structure of the method is such that it naturally fits to a level set representation of the evolving surface. The higher