Stability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes

DOI10.1137/130949531zbMath1339.65173arXiv1602.08055OpenAlexW2282164966MaRDI QIDQ2810564

Jens Lang, L. Kamenski, Weizhang Huang

Publication date: 3 June 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.08055

zbMATH Keywords

finite element methodparabolic equationstability conditionanisotropic meshexplicit one-step method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

High accuracy analysis of an \(H^1\)-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations, Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain, Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes, High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes, Conditioning of the finite volume element method for diffusion problems with general simplicial meshes, Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes

Uses Software

• RKC
• RODAS
• KARDOS
• bamg

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A correction technique for the dispersive effects of mass lumping for transport problems
• Adaptive moving mesh methods
• Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping
• A mixed implicit-explicit finite difference scheme for heat transport in magnetised plasmas
• RKC: An explicit solver for parabolic PDEs
• Metric tensors for anisotropic mesh generation
• An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems
• Unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients
• Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices
• Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems
• Conditioning of finite element equations with arbitrary anisotropic meshes
• Anisotropic mesh adaption for time-dependent problems
• On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces
• Realistic Eigenvalue Bounds for the Galerkin Mass Matrix
• Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix
• Stability of Explicit Runge-Kutta Methods for High Order Finite Element Approximation of Linear Parabolic Equations
• Measuring Mesh Qualities and Application to Variational Mesh Adaptation
• Anisotropic Mesh Refinement: The Conditioning of Galerkin Boundary Element Matrices and Simple Preconditioners