Improved maximum-norm a posteriori error estimates for linear and semilinear parabolic equations

DOI10.1007/s10444-017-9514-3zbMath1378.65167OpenAlexW2592448143MaRDI QIDQ1683221

Natalia Kopteva, Torsten Linss

Publication date: 6 December 2017

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

Full work available at URL: https://doi.org/10.1007/s10444-017-9514-3

zbMATH Keywords

numerical examplesemidiscretizationparabolic problemsCrank-Nicolsonbackward Eulerelliptic reconstructionsmaximum-norm a posteriori error estimates

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Semilinear parabolic equations (35K58)

Related Items (4)

A posteriori error analysis of a fully-discrete finite element method for the wave equation ⋮ A domain decomposition method of Schwarz waveform relaxation type for singularly perturbed nonlinear parabolic problems ⋮ Pointwise a Posteriori Error Bounds for Blow-Up in the Semilinear Heat Equation ⋮ Conditional A Posteriori Error Bounds for High Order Discontinuous Galerkin Time Stepping Approximations of Semilinear Heat Models with Blow-up

Cites Work

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• Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems
• A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems.
• Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem
• Pointwise a posteriori error estimates for monotone semi-linear equations
• Maximum norm a posteriori error estimation for a time-dependent reaction-diffusion problem
• Maximum Norm A Posteriori Error Estimation for Parabolic Problems Using Elliptic Reconstructions
• Numerical Study of Maximum Norm a Posteriori Error Estimates for Singularly Perturbed Parabolic Problems
• Maximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes
• A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems
• Sharply local pointwise a posteriori error estimates for parabolic problems
• Non-Gaussian Aspects of Heat Kernel Behaviour
• Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
• Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $

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