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Adaptive leastsquares methods for convectiondominated diffusionreaction problems Comput. Math. Appl. (IF 2.9) Pub Date : 20240830
Zhiqiang Cai, Binghe Chen, Jing YangThis paper studies adaptive leastsquares finite element methods for convectiondominated diffusionreaction problems. The leastsquares methods are based on the firstorder system of the primal and dual variables with various ways of imposing outflow boundary conditions. The coercivity of the homogeneous leastsquares functionals are established, and the a priori error estimates of the leastsquares

A novel family of Q1finite volume element schemes on quadrilateral meshes Comput. Math. Appl. (IF 2.9) Pub Date : 20240823
Yanhui Zhou, Shuai SuA novel family of isoparametric bilinear finite volume element schemes are constructed and analyzed to solve the anisotropic diffusion problems on general convex quadrilateral meshes. These new schemes are obtained by employing a special quadrature rule to approximate the line integrals in classical finite volume element method. The new quadrature rule is a linear combination of trapezoidal and midpoint

Application of MUSICtype imaging for anomaly detection without background information Comput. Math. Appl. (IF 2.9) Pub Date : 20240822
WonKwang ParkIt has been demonstrated that the MUltiple SIgnal Classification (MUSIC) algorithm is fast, stable, and effective for localizing small anomalies in microwave imaging. For the successful application of MUSIC, exact values of permittivity, conductivity, and permeability of the background must be known. If one of these values is unknown, it will fail to identify the location of an anomaly. However, to

Structure preserving finite element schemes for the NavierStokesCahnHilliard system with degenerate mobility Comput. Math. Appl. (IF 2.9) Pub Date : 20240822
Francisco GuillénGonzález, Giordano TierraIn this work we present two new numerical schemes to approximate the NavierStokesCahnHilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energystable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval goes to zero in terms of a truncation parameter)

Linear stability analysis of a CouettePoiseuille flow: A fluid layer overlying an anisotropic and inhomogeneous porous layer Comput. Math. Appl. (IF 2.9) Pub Date : 20240821
Monisha Roy, Sukhendu Ghosh, G.P. Raja SekharWe investigate the temporal stability analysis of a twolayer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in

A symmetric multigridpreconditioned Krylov subspace solver for Stokes equations Comput. Math. Appl. (IF 2.9) Pub Date : 20240821
Yutian Tao, Eftychios SifakisNumerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability

Numerical analysis of the stochastic Stefan problem Comput. Math. Appl. (IF 2.9) Pub Date : 20240820
Jérôme Droniou, Muhammad Awais Khan, KimNgan LeThe gradient discretisation method (GDM) – a generic framework encompassing many numerical methods – is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by compactness method using discrete functional analysis tools, Skorokhod theorem and the martingale representation theorem. The generic convergence results established

Analysis of a meshless generalized finite difference method for the timefractional diffusionwave equation Comput. Math. Appl. (IF 2.9) Pub Date : 20240820
Lanyu Qing, Xiaolin LiIn this paper, a generalized finite difference method (GFDM) is proposed and analyzed for meshless numerical solution of the timefractional diffusionwave equation. Two order accurate temporal discretization schemes are presented by using the L1 formula and the original H2N2 or fast H2N2 formulas to discretize the timefractional derivative of order . The stability of the temporal discretization

A new scheme for twoway, nesting, quadrilateral grid in an estuarine model Comput. Math. Appl. (IF 2.9) Pub Date : 20240820
Rui Ma, Jianrong Zhu, Cheng QiuGridNesting is a common method of local refinement when using structured quadrilateral grid in estuarine models. Nevertheless, various issues need to be improved, such as the CourantFriedrichsLewy (CFL) limitations of external gravity wave and information exchange between twoway nesting grids. Based on the material conservation law, a novel scheme with Implicit, GridNesting Elevation Solution

Approximation of one and two dimensional nonlinear generalized BenjaminBonaMahony Burgers' equation with local fractional derivative Comput. Math. Appl. (IF 2.9) Pub Date : 20240820
Abdul Ghafoor, Manzoor Hussain, Danyal Ahmad, Shams Ul ArifeenThis study presents, a numerical method for the solutions of the generalized nonlinear BenjaminBonaMahonyBurgers' equation, with variable order local time fractional derivative. This derivative is expressed as a product of two functions, the usual integer order time derivative, and a function of time having a fractional exponent. Then, forward difference approximation is used for time derivative

Superconvergence analysis of finite element approximations to Maxwell's equations in both metamaterials and PMLs Comput. Math. Appl. (IF 2.9) Pub Date : 20240816
Jichun LiThis paper is concerned about the superconvergence analysis for timedependent Maxwell's equations solved by arbitrary order and basis functions on rectangular and cuboid elements. Oneorder higher in spatial convergence is proved for leapfrog finite element schemes developed for solving both Maxwell's equations and perfectly matched layer (PML) models. Numerical results for the 2D PML model solved

Investigation of mesoscopic boundary conditions for lattice Boltzmann method in laminar flow problems Comput. Math. Appl. (IF 2.9) Pub Date : 20240814
Pavel Eichler, Radek Fučík, Pavel StrachotaFor use with the lattice Boltzmann method, the macroscopic boundary conditions need to be transformed into their mesoscopic counterparts. Commonly used mesoscopic boundary conditions use the equilibrium density function, which introduces undesirable artifacts into the numerical solution, especially near interfaces with other types of boundary conditions. In this work, several variants of the mesoscopic

Convection heat and mass transfer of nonNewtonian fluids in porous media with Soret and Dufour effects using a twosided space fractional derivative model Comput. Math. Appl. (IF 2.9) Pub Date : 20240814
Yuehua Jiang, HongGuang Sun, Yong ZhangNonNewtonian fluids within heterogeneous porous media may give rise to complex spatial energy and mass distributions owing to nonlocal mechanisms, the modeling of which remains unclear. This study investigates the natural convection heat and mass transfer of nonNewtonian fluids in porous media, considering the Soret and Dufour effects. A strongly coupled model is developed to quantify the coupled

Low rank approximation method for perturbed linear systems with applications to elliptic type stochastic PDEs Comput. Math. Appl. (IF 2.9) Pub Date : 20240814
Yujun Zhu, Ju Ming, Jie Zhu, Zhongming WangIn this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly reduce the computational load and storage requirements associated with matrix inversion without losing accuracy. To demonstrate the versatility and applicability

A posteriori error estimate of a weak Galerkin finite element method for solving linear elasticity problems Comput. Math. Appl. (IF 2.9) Pub Date : 20240814
Chunmei Liu, Yingying Xie, Liuqiang Zhong, Liping ZhouIn this paper, a residualtype error estimator is proposed and analyzed for a weak Galerkin finite element method for solving linear elasticity problems. The error estimator is proven to be both reliable and efficient, and be used for adaptive refinement. Numerical experiments are presented to illustrate the effectiveness of this error estimator.

A novel bondbased nonlocal diffusion model with matrixvalued coefficients in nondivergence form and its collocation discretization Comput. Math. Appl. (IF 2.9) Pub Date : 20240813
Hao Tian, Junke Lu, Lili JuExisting nonlocal diffusion models are mainly classified into two categories: bondbased models, which involve a singlefold integral and usually simulate isotropic diffusion, and statebased models, which contain a doublefold integral and can additionally prototype anisotropic diffusion. While bondbased models exhibit more computational efficiency, they sometimes could be limited in modeling capabilities

Fixedtime antisynchronization for reactiondiffusion neural networks Comput. Math. Appl. (IF 2.9) Pub Date : 20240813
Radosław Matusik, Anna Michalak, Andrzej NowakowskiWe consider the reactiondiffusion neural network for which coefficients and neural function depend on time and spatial variable. We study fixedtime antisynchronization (FTAS) problem. We develop a dual dynamic programming theory to derive verification theorem allowing to find and verify the best fixedtime for antisynchronization of the system.

Optimal convergence rates in L2 for a first order system least squares finite element method  part II: Inhomogeneous Robin boundary conditions Comput. Math. Appl. (IF 2.9) Pub Date : 20240812
M. Bernkopf, J.M. Melenk 
A decoupled stabilized finite element method for nonstationary stochastic shale oil model based on superhydrophobic material modification Comput. Math. Appl. (IF 2.9) Pub Date : 20240812
Jian Li, Xinyue Zhang, Ruixia LiIn this paper, the effect of random permeability is considered for the real fracture reservoir, hence a stochastic dualporosityNavierStokes model with random permeability is proposed to simulate shale oil problem based on superhydrophobic material modification. Finite element method and Monte Carlo method are used to deal with discrete physical space and probability space, respectively. The decoupled

The Hermitetype virtual element method for second order problem Comput. Math. Appl. (IF 2.9) Pub Date : 20240812
Jikun Zhao, Fengchen Zhou, Bei Zhang, Xiaojing DongIn this paper, we develop the Hermitetype virtual element method to solve the second order problem. A Hermitetype virtual element of degree ≥3 is constructed, which can be taken as an extension of classical Hermite finite element to polygonal meshes. For this virtual element, we rigorously prove some inverse inequalities and the boundedness of basis functions. Further, we prove the interpolation

Error analysis of CrankNicolsonLeapfrog scheme for the twophase CahnHilliardNavierStokes incompressible flows Comput. Math. Appl. (IF 2.9) Pub Date : 20240812
Danchen Zhu, Xinlong Feng, Lingzhi QianIn this paper, the error estimates of the CrankNicolsonLeapfrog (CNLF) timestepping scheme for the twophase CahnHilliardNavierStokes (CHNS) incompressible flow equations based on scalar auxiliary variable (SAV) are strictly proved. Due to the complexity of the multiple variables and the strong coupling of the equations, it is not easy to prove rigorous error estimates. Under the corresponding

Regularization techniques for estimating the spacedependent source in an ndimensional linear parabolic equation using spacedependent noisy data Comput. Math. Appl. (IF 2.9) Pub Date : 20240808
Guillermo Federico Umbricht, Diana RubioIn this article, the mathematical study of the problem of identifying the spacedependent source term, in transport processes given by an dimensional linear parabolic equation, from spacedependent noisy measurements taken at an arbitrary fixed time is conducted. The problem is analytically solved using Fourier techniques, and it is shown that this solution is not stable. Three families of uniparametric

Leastsquares finite element method for the simulation of seaice motion Comput. Math. Appl. (IF 2.9) Pub Date : 20240807
Fleurianne Bertrand, Henrik SchneiderA nonlinear seaice problem is considered in a leastsquares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analyzed. Under additional smoothness assumptions, the leastsquares functional is equivalent to the norm in a neighbourhood of the solution. As the method does not require a compatibility condition between

Mathematical analysis and asymptotic predictions of chemicaldriven swimming living organisms in weighted networks Comput. Math. Appl. (IF 2.9) Pub Date : 20240805
Georges Chamoun, Nahia MouradThis paper derives wellposedness and asymptotic results that provide qualitative information about the behavior, mechanism and strategies used by living organisms to navigate their biological networks. Chemical driven swimming is a captivating phenomenon that is observed in various living organisms like bacteria and protozoa but the problem in weighted networks is more complex, since the equations

Review and computational comparison of adaptive leastsquares finite element schemes Comput. Math. Appl. (IF 2.9) Pub Date : 20240805
Philipp Bringmann 
Surface boundary condition (SBC)based FDTD formulations for lossy dispersive media Comput. Math. Appl. (IF 2.9) Pub Date : 20240801
YongJin Kim, KyungYoung JungThe finitedifference timedomain (FDTD) method is a widely used numerical technique for simulating electromagnetic wave interactions with complex media. Various efficient approaches have been used to analyze complex media, and the surface impedance boundary condition (SIBC) is one of the most powerful techniques in FDTD simulations, allowing efficient electromagnetic modeling of lossy materials. However

Phase field smoothingPINN: A neural network solver for partial differential equations with discontinuous coefficients Comput. Math. Appl. (IF 2.9) Pub Date : 20240731
Rui He, Yanfu Chen, Zihao Yang, Jizu Huang, Xiaofei GuanIn this study, we propose a novel phase field smoothingphysics informed neural network (PFSPINN) approach to efficiently solve partial differential equations (PDEs) with discontinuous coefficients. This method combines the phase field model and the PINN model to overcome the difficulty of low regularity solutions and eliminate the limitations of interface constraints in existing neural network solvers

A fast method and convergence analysis for the MHD flow model of generalized secondgrade fluid Comput. Math. Appl. (IF 2.9) Pub Date : 20240731
Shan Shi, Xiaoyun Jiang, Hui ZhangIn this paper, we investigate the fractional magnetohydrodynamic (MHD) flow model of a generalized secondgrade fluid through a porous medium with Hall current. The fully discrete numerical scheme for solving the model is developed using the formula and Legendre spectral method in time and space, respectively. On the basis of sumofexponentials (SOE) technique, a fast formula for the Caputo fractional

An adaptive stabilized trace finite element method for surface PDEs Comput. Math. Appl. (IF 2.9) Pub Date : 20240731
Timo Heister, Maxim A. Olshanskii, Vladimir YushutinThe paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve lowregularity elliptic problems on levelset surfaces using a shaperegular bulk mesh in the embedding space. Two stabilization variants, gradientjump face and normalgradient volume, are considered for continuous trace spaces of the first and second degrees, based on the polynomial

Iterative solution to the biharmonic equation in mixed form discretized by the Hybrid HighOrder method Comput. Math. Appl. (IF 2.9) Pub Date : 20240730
P.F. Antonietti, P. Matalon, M. VeraniWe consider the solution to the biharmonic equation in mixed form discretized by the Hybrid HighOrder (HHO) methods. The two resulting secondorder elliptic problems can be decoupled via the introduction of a new unknown, corresponding to the boundary value of the solution of the first Laplacian problem. This technique yields a global linear problem that can be solved iteratively via a Krylovtype

Nonconforming quadrilateral finite element analysis for the nonlinear GinzburgLandau equation Comput. Math. Appl. (IF 2.9) Pub Date : 20240726
Huazhao Xie, Dongyang Shi, Qian LiuThis paper is devoted to the study of nonlinear GinzburgLandau equation (GLE) with the nonconforming modified quasiWilson quadrilateral finite element. Based on the special property of this element, that is its consistency error can reach order in the broken norm when the exact solution belongs to , and by use of the interpolated postprocessing technique, the superclose and superconvergence estimates

On a modified Hilbert transformation, the discrete infsup condition, and error estimates Comput. Math. Appl. (IF 2.9) Pub Date : 20240726
Richard Löscher, Olaf Steinbach, Marco ZankIn this paper, we analyze the discrete infsup condition and related error estimates for a modified Hilbert transformation as used in the spacetime discretization of timedependent partial differential equations. It turns out that the stability constant depends linearly on the finite element mesh size . While the ratio decreases as for , numerical results indicate a decay of for some in the polynomial

Analysis of inhomogeneous structures in small and large deformations using the finite elementmeshless coupling method Comput. Math. Appl. (IF 2.9) Pub Date : 20240726
Redouane El Kadmiri, Youssef Belaasilia, Abdelaziz TimesliIn this work, a finite elementmeshless coupling method for modeling the inhomogeneous structures composed of functionally graded materials is presented. Coupling the two methods is usually based on the continuity and equilibrium conditions at the finite elementmeshless interface. In the proposed hybrid method, the equilibrium condition is satisfied by the actionreaction principle to ensure the coupling

A deep learning method for solving multidimensional coupled forward–backward doubly SDEs Comput. Math. Appl. (IF 2.9) Pub Date : 20240726
Sicong Wang, Bin Teng, Yufeng Shi, Qingfeng ZhuForward–backward doubly stochastic differential equations (FBDSDEs) serve as a probabilistic interpretation of stochastic partial differential equations (SPDEs) with diverse applications. Coupled FBDSDEs encounter numerous challenges in numerical approximation compared to forward–backward stochastic differential equations (FBSDEs) and decoupled FBDSDEs, including ensuring the measurability of the numerical

An enriched hybrid highorder method for the Stokes problem with application to flow around submerged cylinders Comput. Math. Appl. (IF 2.9) Pub Date : 20240725
Liam YemmAn enriched hybrid highorder method is designed for the Stokes equations of fluid flow and is fully applicable to generic curved meshes. Minimal regularity requirements of the enrichment spaces are given, and an abstract error analysis of the scheme is provided. The method achieves consistency in the enrichment space and is proven to converge optimally in energy error. The scheme is applied to 2D

Enhanced heat and mass transfer in porous media with OldroydB complex nanofluid flow and heat source Comput. Math. Appl. (IF 2.9) Pub Date : 20240725
Ali Haider, M.S. Anwar, Yufeng Nie, M.S. AlqarniWith their extraordinary ability to conduct heat and their promise to increase heat transfer efficiency, nanofluids have emerged as a major player in the field of fluid technology today. This manuscript delves into the dynamic behavior of timedependent complex OldroydB nanofluids as they traverse between parallel plates within a porous media. Intriguingly, the study introduces captivating elements

Superconvergence analysis of a new stabilized nonconforming finite element method for the Stokes equations Comput. Math. Appl. (IF 2.9) Pub Date : 20240725
Dongyang Shi, Minghao Li, Qili TangThis paper considers a new stabilized finite element method (FEM) of the Stokes equations based on Clément interpolation by the constrained quadrilateral nonconforming rotated  finite element pair. The stabilized term constructed in this method is quite different from those of the existing literature. This method not only has the same attractive computational properties as the conforming stabilized

A numerical scheme for solving an induction heating problem with moving nonmagnetic conductor Comput. Math. Appl. (IF 2.9) Pub Date : 20240724
Van Chien Le, Marián Slodička, Karel Van BockstalThis paper investigates an induction heating problem in a multicomponent system containing a moving nonmagnetic conductor. The electromagnetic process is described by the eddy current model, and the heat transfer process is governed by the convectiondiffusion equation. The two processes are coupled by a restrained Joule heat source. A temporal discretization scheme is introduced to numerically solve

High order numerical methods based on quadratic spline collocation method and averaged L1 scheme for the variableorder time fractional mobile/immobile diffusion equation Comput. Math. Appl. (IF 2.9) Pub Date : 20240724
Xiao Ye, Jun Liu, Bingyin Zhang, Hongfei Fu, Yue LiuIn this paper, we consider the variableorder time fractional mobile/immobile diffusion (TFMID) equation in twodimensional spatial domain, where the fractional order satisfies . We combine the quadratic spline collocation (QSC) method and the formula to propose a QSC scheme. It can be proved that, the QSC scheme is unconditionally stable and convergent with , where , Δ and Δ are the temporal and

A posteriori error analysis for a multidimensional hydrogeological parameter estimation in a time dependent model Comput. Math. Appl. (IF 2.9) Pub Date : 20240723
Hend Ben Ameur, Nizar Kharrat, Mohamed Hedi RiahiWe identify storage coefficient and hydraulic transmissivity in groundwater flow governed by a linear parabolic equation. Both parameters are assumed to be piecewise constant functions in space. The unknowns are the coefficient values as well as the geometry of the zones where these coefficients are constant. The goal of this work is to improve an adaptive parameterization approach for solving an inverse

Analysis of new mixed finite element method for a BarenblattBiot poroelastic model Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
Wenlong He, Jiwei ZhangIn this work, we study the lockingfree numerical method for a BarenblattBiot poroelastic model. When solving by the continuous Galerkin mixed finite element method, the model exists two kind of locking phenomena for special physical parameters. To overcome these locking phenomena, we introduce new variables to reformulate the original problem into a new problem, which exists a builtin mechanism

Cubic and quartic hyperbolic Bsplines comparison for coupled Navier Stokes equation via differential quadrature method  A statistical aspect Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
Mamta KapoorIn this piece of research, cubic and quartic Hyperbolic Bsplines based Differential quadrature methods are implemented for numerical approximation of coupled 2 and 3 NavierStokes equations. The validity of the proposed regimes is tested by the means of different variety of errors such as; error, error, error, and error. It is noticed that most of the time, errors generated by cubic Hyperbolic Bspline

Multirelaxationtime lattice Boltzmann method for anisotropic convectiondiffusion equation with divergencefree velocity field Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
Dinggen Li, Faqiang Li, Bo XuWe propose a multiplerelaxationtime lattice Boltzmann method for anisotropic convectiondiffusion equation with a divergencefree velocity field. In this approach, the convection term is handled as a source term in the lattice Boltzmann evolution equation; thus, the derivation term that may be induced by the convection term disappears. By using the ChapmanEnskog analysis, the anisotropic convectiondiffusion

A generalized energy eigenvalue problem for effectively solving the confined electron states in quantum semiconductor structures via boundary integral analysis Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
J.D. Phan, A.V. PhanThis paper introduces a novel approach for the efficient determination of confined electron states in quantum semiconductor structures through the introduction of a generalized energy eigenvalue problem formulated within the framework of boundary integral analysis. The proposed method enables the direct determination of the energy eigenvalues and normalized wavefunctions for bound quantum states. The

Iterative algorithms for partitioned neural network approximation to partial differential equations Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
Hee Jun Yang, Hyea Hyun KimTo enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain

Semilocal convergence of Chebyshev Kurchatov type methods for nondifferentiable operators Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
Sonia Yadav, Sukhjit Singh, R.P. Badoni, Ajay Kumar, Mehakpreet SinghIn this study, the new semilocal convergence for the family of Chebyshev Kurchatov type methods is proposed under weaker conditions. The convergence analysis demands conditions on the initial approximation, auxiliary point, and the underlying operator (Argyros et al. (2017) ). By utilizing the notion of auxiliary point in convergence conditions, the convergence domains are obtained where the existing

Numerical aspects of Casimir energy computation in acoustic scattering Comput. Math. Appl. (IF 2.9) Pub Date : 20240722
Xiaoshu Sun, Timo Betcke, Alexander StrohmaierComputing the Casimir force and energy between objects is a classical problem of quantum theory going back to the 1940s. Several different approaches have been developed in the literature often based on different physical principles. Most notably a representation of the Casimir energy in terms of determinants of boundary layer operators makes it accessible to a numerical approach. In this paper, we

A comparative numerical study of finite element methods resulting in mass conservation for Poisson's problem: Primal hybrid, mixed and their hybridized formulations Comput. Math. Appl. (IF 2.9) Pub Date : 20240718
Victor B. Oliari, Ricardo J. Hancco Ancori, Philippe R.B. DevlooThis paper presents a numerical comparison of finiteelement methods resulting in local mass conservation at the element level for Poisson's problem, namely the primal hybrid and mixed methods. These formulations result in an indefinite system. Alternative formulations yielding a positivedefinite system are obtained after hybridizing each method. The choice of approximation spaces yields methods with

New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite element Comput. Math. Appl. (IF 2.9) Pub Date : 20240718
Francesco Dell'Accio, Allal Guessab, Federico NudoIn this paper, we introduce quadratic and cubic polynomial enrichments of the classical Crouzeix–Raviart finite element, with the aim of constructing accurate approximations in such enriched elements. To achieve this goal, we respectively add three and seven weighted line integrals as enriched degrees of freedom. For each case, we present a necessary and sufficient condition under which these augmented

Analysis of variabletimestep BDF2 combined with the fast twogrid finite element algorithm for the FitzHughNagumo model Comput. Math. Appl. (IF 2.9) Pub Date : 20240717
Xinyuan Liu, Nan Liu, Yang Liu, Hong LiIn this article, a fast numerical method is developed for solving the FitzHughNagumo (FHN) model by combining twogrid finite element (TGFE) algorithm in space with a linearized variabletimestep (VTS) twostep backward differentiation formula (BDF2) in time. This algorithm mainly included two steps: firstly, the nonlinear coupled system on the coarse grid is solved by a nonlinear iteration; secondly

Heat transfer effect on the ferrofluid flow in a curved cylindrical annular duct under the influence of a magnetic field Comput. Math. Appl. (IF 2.9) Pub Date : 20240717
Panteleimon A. Bakalis, Polycarpos K. Papadopoulos, Panayiotis VafeasThe current research, which can be employed in various engineering applications, is involved with the investigation of the heat transfer effect on the laminar and fully developed ferrohydrodynamic flow into a curved annular cylindrical duct, when a constant very strong transverse magnetic field is applied. The numerical solution of the involved constitutive partial differential equations, i.e. the

A finite element contour integral method for computing the resonances of metallic grating structures with subwavelength holes Comput. Math. Appl. (IF 2.9) Pub Date : 20240717
Yingxia Xi, Junshan Lin, Jiguang SunWe consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of several length scales in problem geometry and material contrast. We discretize the partial differential equation model over the truncated domain using the finite

A discreteordinates variational nodal method for heterogeneous neutron Boltzmann transport problems Comput. Math. Appl. (IF 2.9) Pub Date : 20240716
Qizheng Sun, Xiaojing Liu, Xiang Chai, Hui He, Tengfei ZhangThis study introduces an unstructured variational nodal method (UVNMS), also recognized as the hybridized discontinuous Galerkin (HDG) method, for solving heterogeneous neutron Boltzmann transport problems. The UVNMS solves the variational formulation of neutron Boltzmann transport equation (NBTE) by meshing the problem domain with nonoverlapping nodes, i.e. the meshes. Lagrange multipliers are

Multiple unequal cracks between a functionally graded piezoelectric layer and a piezoelectric substrate by distributed strain nuclei Comput. Math. Appl. (IF 2.9) Pub Date : 20240716
R. Boroujerdi, M.M. MonfaredIn this paper, distributed strain nucleus is presented to compute the modes I/II stress intensity factors (SIFs) and electric displacement intensity factors (EDIFs) for multiple unequal cracks placed between a functionally graded piezoelectric materials (FGPMs) and a piezoelectric halfplane. Employing the Fourier transform, the governing electroelastic equations are solved in terms of the Burgers

A highorder arbitrary LagrangianEulerian discontinuous Galerkin method for compressible flows in twodimensional Cartesian and cylindrical coordinates Comput. Math. Appl. (IF 2.9) Pub Date : 20240716
Xiaolong Zhao, Shijun Zou, Xijun Yu, Dongyang Shi, Shicang SongIn this paper, a highorder direct arbitrary LagrangianEulerian (ALE) discontinuous Galerkin (DG) scheme is developed for compressible fluid flows in twodimensional (2D) Cartesian and cylindrical coordinates. The scheme in 2D cylindrical coordinates is based on the control volume approach and it can preserve the conservation property for all the conserved variables including mass, momentum and total

Convergence of adaptive mixed interior penalty discontinuous Galerkin methods for [formula omitted]elliptic problems Comput. Math. Appl. (IF 2.9) Pub Date : 20240716
Kai Liu, Ming Tang, Xiaoqing Xing, Liuqiang ZhongIn this paper, we study the convergence of adaptive mixed interior penalty discontinuous Galerkin method for elliptic problems. We first get the mixed model of elliptic problem by introducing a new intermediate variable. Then we discuss the continuous variational problem and discrete variational problem, which based on interior penalty discontinuous Galerkin approximation. Next, we construct the

Adaptive sampling points based multiscale residual network for solving partial differential equations Comput. Math. Appl. (IF 2.9) Pub Date : 20240716
Jie Wang, Xinlong Feng, Hui XuPhysicsinformed neural networks (PINNs) have shown remarkable achievements in solving partial differential equations (PDEs). However, their performance is limited when encountering oscillatory part in the solutions of PDEs. Therefore, this paper proposes a multiscale deep neural network with periodic activation function to achieve highfrequency to lowfrequency conversion, which can capture the

A parallel stabilized finite element method for the NavierStokes problem Comput. Math. Appl. (IF 2.9) Pub Date : 20240714
Jing Han, Guangzhi Du, Shilin MiIn this article, we mainly propose and analyze a parallel stabilized finite element algorithm based upon twogrid discretization for the NavierStokes problem. The lowest equalorder finite element pairs are considered for the finite element discretization and a stabilized term based on two local Gauss integrations is introduced to circumvent the discrete infsup condition. The main idea is to utilize

Onelevel and twolevel operator splitting methods for the unsteady incompressible micropolar fluid equations with double diffusion convection Comput. Math. Appl. (IF 2.9) Pub Date : 20240714
Demin Liu, Youlei LiangIn this paper, a onelevel operator splitting method (OOSM) and a twolevel operator splitting method (TOSM) for the twodimensional or threedimensional (2D/3D) unsteady incompressible micropolar fluid equations with double diffusion convection (IMFDDC) are proposed and analyzed. Firstly, a OOSM is constructed, which consists of five steps. The projection strategy is adopted to get the values of linear

A reducedorder method for geometrically nonlinear analysis of the wingupperskin panels in the presence of buckling Comput. Math. Appl. (IF 2.9) Pub Date : 20240714
Ke Liang, Zhen Yin, Qiuyang HaoThinwalled structures, i.e. the wingupperskin panels, are prone to buckling accompanied by a significantly large outofplane deflection. The computational efficiency of the conventional finite element based fullorder method is not satisfactory for nonlinear buckling problems of the structure. In this work, the skin panels on the upper surface of the wing butt box are selected using a submodeling