A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems.

DOI10.1007/s10492-014-0052-8zbMath1340.65163OpenAlexW2077557885MaRDI QIDQ464703

Torsten Linss

Publication date: 29 October 2014

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

Full work available at URL: http://hdl.handle.net/10338.dmlcz/143769

zbMATH Keywords

singular perturbationfinite element methodmesh adaptationreaction-diffusion problem

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (7)

Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension ⋮ Improved maximum-norm a posteriori error estimates for linear and semilinear parabolic equations ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ A posteriori maximum-norm error bounds for the biquadratic spline collocation method applied to reaction-diffusion problems ⋮ Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems ⋮ The error estimates of spectral methods for 1-dimension singularly perturbed problem ⋮ 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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• A note on the energy norm for a singularly perturbed model problem
• Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem
• Layer-adapted meshes for reaction-convection-diffusion problems
• \(hp\)-finite element methods for singular perturbations
• Pointwise a posteriori error estimates for monotone semi-linear equations
• 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
• A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction-diffusion problem
• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems
• A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
• Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem

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