Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

DOI10.1007/s00211-017-0889-3zbMath1379.65084arXiv1810.09211OpenAlexW2611228231MaRDI QIDQ1679209

Natalia Kopteva

Publication date: 8 November 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09211

zbMATH Keywords

singular perturbationweak formulationenergy-normquasi-interpolation operatora posteriori errorlinear finite elementsanisotropic triangulationsharp layerssemilinear reaction-diffusion

Mathematics Subject Classification ID

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) Semilinear elliptic equations (35J61)

Related Items (5)

Pointwise A Posteriori Error Estimates for Discontinuous Galerkin Methods for Singularly Perturbed Reaction-Diffusion Equations ⋮ Lower a posteriori error estimates on anisotropic meshes ⋮ Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms ⋮ A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems ⋮ Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems

Cites Work

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• Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems
• Maximum norm a posteriori error estimate for a 3D singularly perturbed semilinear reaction-diffusion problem
• Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation
• Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes
• An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
• An a posteriori error estimator for anisotropic refinement
• Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations
• Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
• Maximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem
• New anisotropic a priori estimates
• Robust a posteriori error estimation for a singularly perturbed reaction--diffusion equation on anisotropic tetrahedral meshes

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