Superconvergence on a hybrid mesh for singularly perturbed problems with exponential layers

DOI10.1002/zamm.200510264zbMath1097.65107OpenAlexW2016397973MaRDI QIDQ5485462

Hans-Goerg Roos

Publication date: 30 August 2006

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.200510264

zbMATH Keywords

singular perturbationfinite elementssuperconvergencereaction-diffusion equationexponential boundary layers

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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 (10)

Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers ⋮ Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem ⋮ Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Nitsche-mortaring for singularly perturbed convection-diffusion problems ⋮ Uniform supercloseness of Galerkin finite element method for convection-diffusion problems with characteristic layers ⋮ Convergence in \(L^{2}\) norm of the SDFEM on a Shishkin triangular mesh for problems with characteristic layers ⋮ Galerkin finite element methods for convection-diffusion problems with exponential layers on Shishkin triangular meshes and hybrid meshes ⋮ Optimal Order $L^2$ Error Estimate of SDFEM on Shishkin Triangular Meshes for Singularly Perturbed Convection-Diffusion Equations ⋮ Supercloseness of continuous interior penalty methods on Shishkin triangular meshes and hybrid meshes for singularly perturbed problems with characteristic layers

Cites Work

• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy

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