A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps

DOI10.1134/S096554252011007XzbMath1453.65411OpenAlexW3111693613MaRDI QIDQ2214602

V. G. Korneev

Publication date: 10 December 2020

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s096554252011007x

zbMATH Keywords

finite element methodsharp boundsa posteriori error boundspiecewise constant reaction coefficientsingularly perturbed fourth-order elliptic equations

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with low regular coefficients and/or low regular data (35R05) Boundary value problems for linear higher-order PDEs (35G15)

Related Items (1)

On error control at numerical solution of forth order elliptic equations with strongly discontinuous reaction coefficient

Cites Work

• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-love plate
• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• A posteriori error estimates for the Morley plate bending element
• A posteriori error estimates for fourth-order elliptic problems
• Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension
• A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems
• Some a posteriori error bounds for numerical solutions of plate in bending problems
• On error control in the numerical solution of reaction-diffusion equation
• On the accuracy of a posteriori functional error majorants for approximate solutions of elliptic equations
• Zur Konvergenz von Näherungsverfahren bezüglich verschiedener Normen. (On convergence of approximation methods with respect to various norms)
• An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems
• Residual-based a posteriori error estimator for the mixed finite element approximation of the biharmonic equation
• An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
• Ultraconvergence of the patch recovery technique
• Analysis of recovery type a posteriori error estimators for mildly structured grids
• Dirichlet–Dirichlet Domain Decomposition Methods for Elliptic Problems
• A posteriori error estimates for finite element approximations of the Cahn-Hilliard equation and the Hele-Shaw flow
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