Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains

DOI10.1016/j.camwa.2017.03.015zbMath1397.65264arXiv1610.09211OpenAlexW3020871892WikidataQ115580791 ScholiaQ115580791MaRDI QIDQ1663821

Markus Faustmann, Jens Markus Melenk

Publication date: 24 August 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.09211

zbMATH Keywords

singular perturbationuniform estimatesbalanced normhigh-order FEM

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

Related Items (3)

Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons ⋮ Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons ⋮ Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems

Uses Software

• Netgen
• NGSolve

Cites Work

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• Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations
• NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
• \(hp\)-finite element methods for singular perturbations
• The \(hp\) finite element method for problems in mechanics with boundary layers
• Error estimation in a balanced norm for a convection-diffusion problem with two different boundary layers
• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Thep-Version of the Finite Element Method
• On the robust exponential convergence of hp finite element methods for problems with boundary layers
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems

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