Robust a posteriori error estimation for a singularly perturbed reaction--diffusion equation on anisotropic tetrahedral meshes

DOI10.1023/A:1014248711347zbMath1049.65121OpenAlexW278206857MaRDI QIDQ5959278

Gerd Kunert

Publication date: 26 March 2002

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1014248711347

zbMATH Keywords

numerical examplesingular perturbationerror boundsanisotropic solutionreaction diffusion equationanisotropic finite element meshesmatching functionstretched elements

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)

Related Items (28)

Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems ⋮ Maximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes ⋮ A Study on Anisotropic Mesh Adaptation for Finite Element Approximation of Eigenvalue Problems with Anisotropic Diffusion Operators ⋮ A posteriori error estimation based on conservative flux reconstruction for nonconforming finite element approximations to a singularly perturbed reaction-diffusion problem on anisotropic meshes ⋮ Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ A posteriori error estimation for a finite volume discretization on anisotropic meshes ⋮ Robust a posteriori error estimates for conforming discretizations of a singularly perturbed reaction-diffusion problem on anisotropic meshes ⋮ A posteriori error estimation of residual type for anisotropic diffusion-convection-reaction problems ⋮ Lower a posteriori error estimates on anisotropic meshes ⋮ Maximum norm a posteriori error estimate for a 3D singularly perturbed semilinear reaction-diffusion problem ⋮ An anisotropic pressure-stabilized finite element method for incompressible flow problems ⋮ A posteriori error estimates for Hughes stabilized SUPG technique and adaptive refinement for a convection-diffusion problem ⋮ A posteriori maximum-norm error bounds for the biquadratic spline collocation method applied to reaction-diffusion problems ⋮ Anisotropic mesh adaptation in computational fluid dynamics: application to the advection-diffusion-reaction and the Stokes problems ⋮ A POSTERIORI ERROR ESTIMATION FOR THE STOKES PROBLEM: ANISOTROPIC AND ISOTROPIC DISCRETIZATIONS ⋮ A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates ⋮ Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes ⋮ Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes ⋮ Guaranteed and robusta posteriorierror estimates for singularly perturbed reaction–diffusion problems ⋮ Robust a posteriori error estimation for the Maxwell equations ⋮ Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems ⋮ Nitsche type mortaring for singularly perturbed reaction-diffusion problems ⋮ An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes ⋮ The uniform saturation property for a singularly perturbed reaction-diffusion equation ⋮ The error estimates of spectral methods for 1-dimension singularly perturbed problem ⋮ A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations ⋮ Guaranteed a posteriori error estimates for nonconforming finite element approximations to a singularly perturbed reaction-diffusion problem

This page was built for publication: Robust a posteriori error estimation for a singularly perturbed reaction--diffusion equation on anisotropic tetrahedral meshes