Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations

DOI10.1090/S0025-5718-2014-02820-2zbMath1301.65122OpenAlexW2077251597MaRDI QIDQ3189413

Natalia Kopteva

Publication date: 10 September 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2014-02820-2

zbMATH Keywords

singular perturbationBakhvalov meshShishkin meshfinite differencereaction-diffusion equationmaximum normlinear finite elementsanisotropic triangulation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (6)

Maximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes ⋮ Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes ⋮ Why Do We Need Voronoi Cells and Delaunay Meshes? ⋮ Uniform convergence of finite element method on Bakhvalov-type triangular mesh for a singularly perturbed problem featuring exponential layers ⋮ Why do we need Voronoi cells and Delaunay meshes? Essential properties of the Voronoi finite volume method ⋮ How accurate are finite elements on anisotropic triangulations in the maximum norm?

Cites Work

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• Asymptotic error expansion and Richardson extrapolation for linear finite elements
• Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm
• Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
• On Optimal Interpolation Triangle Incidences
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
• On the Quasi-Optimality in $L_\infty$ of the $\overset{\circ}{H}^1$-Projection into Finite Element Spaces*
• Optimal Triangular Mesh Generation by Coordinate Transformation
• Anisotropic mesh adaptation for numerical solution of boundary value problems
• A parameter robust numerical method for a two dimensional reaction-diffusion problem

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