Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping

DOI10.1016/j.cam.2011.05.030zbMath1269.65084OpenAlexW2004719710MaRDI QIDQ651917

Liyong Zhu, Qiang Du

Publication date: 19 December 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.05.030

zbMATH Keywords

stabilityfinite element methodnumerical experimentsparabolic equationunstructured meshmass lumpingstable time step size

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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

Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes ⋮ Stability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes ⋮ Conditioning of the finite volume element method for diffusion problems with general simplicial meshes ⋮ Sharp Bounds on the Smallest Eigenvalue of Finite Element Equations with Arbitrary Meshes without Regularity Assumptions ⋮ Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Higher-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation
• 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
• Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping
• On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces
• Bounds on eigenvalues of finite element systems
• Mesh and solver co‐adaptation in finite element methods for anisotropic problems