Maximum norm a posteriori error estimate for a 3D singularly perturbed semilinear reaction-diffusion problem

DOI10.1007/s10444-010-9163-2zbMath1319.65105OpenAlexW2066672987MaRDI QIDQ647424

Natalia Kopteva, Naresh M. Chadha

Publication date: 23 November 2011

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

Full work available at URL: https://strathprints.strath.ac.uk/44819/

zbMATH Keywords

singular perturbationGreen's functionfinite differenceslayer-adapted mesha posteriori error estimatenumerical resultmaximum normsemilinear reaction-diffusion equationno mesh aspect ratio conditionnonuniform tensor-product meshes

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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Semilinear elliptic equations (35J61) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

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Cites Work

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• Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem
• Hölder estimates for Green's functions on convex polyhedral domains and their applications to finite element methods
• On monotone iterative methods for a nonlinear singularly perturbed reaction--diffusion problem.
• Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes
• Elliptic partial differential equations of second order
• Linear and quasilinear elliptic equations
• Maximum Norm A Posteriori Error Estimates for a One-Dimensional Convection-Diffusion Problem
• Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm
• Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
• On Optimal Interpolation Triangle Incidences
• Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem
• On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
• Optimal Triangular Mesh Generation by Coordinate Transformation
• Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems
• AN ADAPTIVE FINITE ELEMENT METHOD WITH EFFICIENT MAXIMUM NORM ERROR CONTROL FOR ELLIPTIC PROBLEMS
• Pointwise a Posteriori Error Estimates for Elliptic Problems on Highly Graded Meshes
• Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles
• A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
• Anisotropic mesh adaptation for numerical solution of boundary value problems
• Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem
• A parameter robust numerical method for a two dimensional reaction-diffusion problem
• Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods
• The SDFEM on Shishkin meshes for linear convection-diffusion problems
• Robust a posteriori error estimation for a singularly perturbed reaction--diffusion equation on anisotropic tetrahedral meshes