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Tensor completion via multi-directional partial tensor nuclear norm with total variation regularization Calcolo (IF 1.7) Pub Date : 2024-03-04 Rong Li, Bing Zheng
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A Gauss–Newton method for mixed least squares-total least squares problems Calcolo (IF 1.7) Pub Date : 2024-03-01 Qiaohua Liu, Shan Wang, Yimin Wei
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Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh Calcolo (IF 1.7) Pub Date : 2024-02-28
Abstract Some popular stabilization techniques, such as nonsymmetric interior penalty Galerkin (NIPG) method, have important application value in computational fluid dynamics. In this paper, we analyze a NIPG method on Shishkin mesh for a singularly perturbed convection diffusion problem, which is a typical simplified fluid model. According to the characteristics of the solution, the mesh and the numerical
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Numerical methods for the forward and backward problems of a time-space fractional diffusion equation Calcolo (IF 1.7) Pub Date : 2024-02-21 Xiaoli Feng, Xiaoyu Yuan, Meixia Zhao, Zhi Qian
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Optimal learning Calcolo (IF 1.7) Pub Date : 2024-02-19 Peter Binev, Andrea Bonito, Ronald DeVore, Guergana Petrova
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Discrete duality finite volume scheme for a generalized Joule heating problem Calcolo (IF 1.7) Pub Date : 2024-02-07 Mustapha Bahari, El-Houssaine Quenjel, Mohamed Rhoudaf
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Discontinuous Galerkin methods for Stokes equations under power law slip boundary condition: a priori analysis Calcolo (IF 1.7) Pub Date : 2024-02-01 Djoko Kamdem Jules, Gidey Hagos, Koko Jonas, Sayah Toni
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Optimal approximation of infinite-dimensional holomorphic functions Calcolo (IF 1.7) Pub Date : 2024-01-29 Ben Adcock, Nick Dexter, Sebastian Moraga
Over the several decades, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computational uncertainty quantification. This is primarily due to the relevance of functions that are solutions to parametric differential equations in various fields, e.g. chemistry, economics, engineering, and physics. While
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Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon Calcolo (IF 1.7) Pub Date : 2024-01-11 Yanchen He, Christoph Schwab
In an open, bounded Lipschitz polygon \(\Omega \subset \mathbb {R}^2\), we establish weighted analytic regularity for a semilinear, elliptic PDE with analytic nonlinearity and subject to a source term f which is analytic in \(\Omega \). The boundary conditions on each edge of \(\partial \Omega \) are either homogeneous Dirichlet or homogeneous Neumann BCs. The presently established weighted analytic
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The Hermite-type virtual element method with interior penalty for the fourth-order elliptic problem Calcolo (IF 1.7) Pub Date : 2024-01-03 Jikun Zhao, Teng Chen, Bei Zhang, Xiaojing Dong
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Error estimates of invariant-preserving difference schemes for the rotation-two-component Camassa–Holm system with small energy Calcolo (IF 1.7) Pub Date : 2024-01-02 Qifeng Zhang, Jiyuan Zhang, Zhimin Zhang
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An algorithm for the spectral radius of weakly essentially irreducible nonnegative tensors Calcolo (IF 1.7) Pub Date : 2024-01-02 Guimin Liu, Hongbin Lv
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A convection–diffusion problem with a large shift on Durán meshes Calcolo (IF 1.7) Pub Date : 2023-12-28 Mirjana Brdar, Sebastian Franz, Hans-Görg Roos
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$$L^2(I;H^1(\Omega )^d)$$ and $$L^2(I;L^2(\Omega )^d)$$ best approximation type error estimates for Galerkin solutions of transient Stokes problems Calcolo (IF 1.7) Pub Date : 2023-12-29 Dmitriy Leykekhman, Boris Vexler
In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in \(L^2(I;L^2(\Omega )^d)\) and \(L^2(I;H^1(\Omega )^d)\) norms. These estimates fill the gap in the error analysis of the transient Stokes problems and have a number of applications. The analysis naturally extends to inhomogeneous parabolic problems. The best type \(L^2(I;H^1(\Omega
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On the positivity of the discrete Green’s function for unstructured finite element discretizations in three dimensions Calcolo (IF 1.7) Pub Date : 2023-12-22 Andrew P. Miller
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A class of two stage multistep methods in solutions of time dependent parabolic PDEs Calcolo (IF 1.7) Pub Date : 2023-12-21 Moosa Ebadi, Mohammad Shahriari
In this manuscript, a new class of high-order multistep methods on the basis of hybrid backward differentiation formulas (BDF) have been illustrated for the numerical solutions of systems of ordinary differential equations (ODEs) arising from semi-discretization of time dependent partial differential equations. Order and stability analysis of the methods have been discussed in detail. By using an off-step
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High-order schemes based on extrapolation for semilinear fractional differential equation Calcolo (IF 1.7) Pub Date : 2023-12-11 Yuhui Yang, Charles Wing Ho Green, Amiya K. Pani, Yubin Yan
By rewriting the Riemann–Liouville fractional derivative as Hadamard finite-part integral and with the help of piecewise quadratic interpolation polynomial approximations, a numerical scheme is developed for approximating the Riemann–Liouville fractional derivative of order \(\alpha \in (1,2).\) The error has the asymptotic expansion \( \big ( d_{3} \tau ^{3- \alpha } + d_{4} \tau ^{4-\alpha } + d_{5}
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Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms Calcolo (IF 1.7) Pub Date : 2023-11-29 S. Priyadarshana, J. Mohapatra, H. Ramos
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Accurate and efficient numerical methods for the nonlinear Schrödinger equation with Dirac delta potential Calcolo (IF 1.7) Pub Date : 2023-11-20 Xuanxuan Zhou, Yongyong Cai, Xingdong Tang, Guixiang Xu
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Elliptic polytopes and invariant norms of linear operators Calcolo (IF 1.7) Pub Date : 2023-11-17 Thomas Mejstrik, Valdimir Yu. Protasov
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Fast barycentric rational interpolations for complex functions with some singularities Calcolo (IF 1.7) Pub Date : 2023-11-15 Shunfeng Yang, Shuhuang Xiang
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A linear algebra perspective on the random multi-block ADMM: the QP case Calcolo (IF 1.7) Pub Date : 2023-11-15 Stefano Cipolla, Jacek Gondzio
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On greedy randomized block Gauss–Seidel method with averaging for sparse linear least-squares problems Calcolo (IF 1.7) Pub Date : 2023-11-13 Yimou Liao, Tianxiu Lu
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A posteriori analysis for a mixed formulation of the Stokes spectral problem Calcolo (IF 1.7) Pub Date : 2023-11-13 Felipe Lepe, Jesus Vellojin
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A Banach spaces-based mixed finite element method for the stationary convective Brinkman–Forchheimer problem Calcolo (IF 1.7) Pub Date : 2023-10-20 Sergio Caucao, Gabriel N. Gatica, Luis F. Gatica
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Two-dimensional Jacobi pseudospectral quadrature solutions of two-dimensional fractional Volterra integral equations Calcolo (IF 1.7) Pub Date : 2023-10-18 A. K. Mittal
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A weighted ADI scheme with variable time steps for diffusion-wave equations Calcolo (IF 1.7) Pub Date : 2023-10-09 Pin Lyu, Seakweng Vong
We study a weighted alternating direction implicit (ADI) numerical method with variable time steps for two-dimensional diffusion-wave equations. The variable-step Alikhanov formula is employed to approximate the fractional derivatives in an equivalent coupled equations which is generated by the symmetric fractional-order reduction (SFOR) method. By adding a weighted small external term, we obtain a
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A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes Calcolo (IF 1.7) Pub Date : 2023-10-06 Naresh Kumar, Bhupen Deka
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Preconditioning of discrete state- and control-constrained optimal control convection-diffusion problems Calcolo (IF 1.7) Pub Date : 2023-10-08 Ivo Dravins, Maya Neytcheva
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A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation Calcolo (IF 1.7) Pub Date : 2023-09-23 Sudheer Mishra, E. Natarajan
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Local projection stabilized finite element methods for advection–reaction problems Calcolo (IF 1.7) Pub Date : 2023-09-12 Deepika Garg, Sashikumaar Ganesan
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A macro-bubble enriched P1–P0 finite element for the Stokes equations on triangular and tetrahedral meshes Calcolo (IF 1.7) Pub Date : 2023-08-24 Shangyou Zhang
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Conditioning of Fourier sums on a quadratic curve Calcolo (IF 1.7) Pub Date : 2023-08-05 Phung Van Manh
The stability property of representations of the Fourier sums on a quadratic curve is measured through a condition number. We analyze the conditioning of the continuous Fourier sums and the discrete Fourier sums on the unit circle and the standard parabola. We give an upper bound for the conditioning in terms of norms of two families of orthogonal polynomials in one variable. We establish explicit
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Polynomial time $$\rho $$ -locally maximum volume search Calcolo (IF 1.7) Pub Date : 2023-08-03 Alexander Osinsky
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ADI Finite Element Galerkin Methods for Two-dimensional Tempered Fractional Integro-differential Equations Calcolo (IF 1.7) Pub Date : 2023-08-03 Wenlin Qiu, Graeme Fairweather, Xuehua Yang, Haixiang Zhang
Three alternating direction implicit (ADI) finite element Galerkin methods for solving two-dimensional tempered fractional integro-differential equations are formulated and analyzed. For the time discretization, these methods are based on the backward Euler scheme, the Crank–Nicolson scheme and the second-order backward differentiation formula, respectively, each combined with an appropriate convolution
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Energy-norm and balanced-norm supercloseness error analysis of a finite volume method on Shishkin meshes for singularly perturbed reaction–diffusion problems Calcolo (IF 1.7) Pub Date : 2023-07-28 Xiangyun Meng, Martin Stynes
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Accurate computation of eigenvalues of generalized sign regular quasi-Said–Ball–Vandermonde matrices Calcolo (IF 1.7) Pub Date : 2023-07-21 Yebo Xiong
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Deflated and restarted Krylov subspace methods for Sylvester tensor equations Calcolo (IF 1.7) Pub Date : 2023-07-11 Ying Gu, Gang Wu, Xin Zhang
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A stable and $$H^1$$ -conforming divergence-free finite element pair for the Stokes problem using isoparametric mappings Calcolo (IF 1.7) Pub Date : 2023-06-27 Michael Neilan, M. Baris Otus
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Augmented spectral formulation for the Stokes problem with variable viscosity and mixed boundary conditions Calcolo (IF 1.7) Pub Date : 2023-06-23 C. Bousbiat, Y. Daikh, S. Maarouf, D. Yakoubi
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Further results on tensor nuclear norms Calcolo (IF 1.7) Pub Date : 2023-06-15 Chao Zeng
Several basic properties of tensor nuclear norms are established in [S. Friedland and L.-H. Lim, Math. Comp., 87 (2018), pp. 1255–1281]. In this work, we give further studies on tensor nuclear norms. We present some special cases of tensor nuclear decompositions. We list some examples to show basic relationships among tensor rank, orthogonal rank and nuclear rank. Spectral and nuclear norms of Hermitian
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The Fréchet derivative of the tensor t-function Calcolo (IF 1.7) Pub Date : 2023-06-16 Kathryn Lund, Marcel Schweitzer
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On polynomials generated by a four-term recurrence relation and linear coefficients Calcolo (IF 1.7) Pub Date : 2023-06-15 Vanessa Botta, Eduardo Fornazieri Filho
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Cohomology of the discrete de Rham complex on domains of general topology Calcolo (IF 1.7) Pub Date : 2023-05-24 Daniele A. Di Pietro, Jérôme Droniou, Silvano Pitassi
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Numerical solution of the space-time fractional diffusion equation based on fractional reproducing kernel collocation method Calcolo (IF 1.7) Pub Date : 2023-05-18 Rui Sun, Jiabao Yang, Huanmin Yao
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Mean-square convergence and stability of compensated stochastic theta methods for jump-diffusion SDEs with super-linearly growing coefficients Calcolo (IF 1.7) Pub Date : 2023-05-11 Yiling Wang, Ziheng Chen, Mengyao Niu, Yuanling Niu
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A virtual element method for the elasticity problem allowing small edges Calcolo (IF 1.7) Pub Date : 2023-04-30 Danilo Amigo, Felipe Lepe, Gonzalo Rivera
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Mesh quality agglomeration algorithm for the virtual element method applied to discrete fracture networks Calcolo (IF 1.7) Pub Date : 2023-04-28 Tommaso Sorgente, Fabio Vicini, Stefano Berrone, Silvia Biasotti, Gianmarco Manzini, Michela Spagnuolo
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Iterative optimal solutions of linear matrix equations for hyperspectral and multispectral image fusing Calcolo (IF 1.7) Pub Date : 2023-04-27 Frank Uhlig, An-Bao Xu
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Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part I Calcolo (IF 1.7) Pub Date : 2023-04-25 O. Boussoufa, Y. Daikh, D. Yakoubi
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Positivity preserving truncated scheme for the stochastic Lotka–Volterra model with small moment convergence Calcolo (IF 1.7) Pub Date : 2023-04-25 Yongmei Cai, Qian Guo, Xuerong Mao
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Spectral approximation methods for nonlinear integral equations with non-smooth kernels Calcolo (IF 1.7) Pub Date : 2023-04-23 C. Allouch, D. Sbibih, M. Tahrichi
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On the convergence of numerical integration as a finite matrix approximation to multiplication operator Calcolo (IF 1.7) Pub Date : 2023-04-04 Juha Sarmavuori, Simo Särkkä
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An adaptive immersed finite element method for linear parabolic interface problems with nonzero flux jump Calcolo (IF 1.7) Pub Date : 2023-03-13 Tanushree Ray, Rajen Kumar Sinha
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Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems Calcolo (IF 1.7) Pub Date : 2023-03-13 Fazhan Geng, Xinyuan Wu
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The infinite Lanczos method for symmetric nonlinear eigenvalue problems Calcolo (IF 1.7) Pub Date : 2023-03-05 Giampaolo Mele
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Gradient recovery based a posteriori error estimator for the adaptive direct discontinuous Galerkin method Calcolo (IF 1.7) Pub Date : 2023-02-26 Huihui Cao, Yunqing Huang, Nianyu Yi
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Spectral methods in space and time for parabolic problems on semi-infinite domains Calcolo (IF 1.7) Pub Date : 2023-02-21 Xuhong Yu, Zhongqing Wang
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New error estimates of Lagrange–Galerkin methods for the advection equation Calcolo (IF 1.7) Pub Date : 2023-02-09 Rodolfo Bermejo, Jaime Carpio, Laura Saavedra