Local projection stabilisation on \(S\)-type meshes for convection-diffusion problems with characteristic layers

DOI10.1007/s00607-010-0079-yzbMath1203.65226OpenAlexW2062279878MaRDI QIDQ971931

Sebastian Franz, Gunar Matthies

Publication date: 17 May 2010

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-010-0079-y

zbMATH Keywords

convergenceGalerkin methodsingular perturbationfinite elementconvection-diffusion problemsShishkin meshesexponential layerslocal projectioncharacteristic layers

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (17)

Iterative analytic approximation to nonlinear convection dominated systems ⋮ Analysis of a family of continuous-discontinuous Galerkin FEM for convection-diffusion problems ⋮ Convergence of local projection stabilisation finite element methods for convection-diffusion problems on layer-adapted meshes ⋮ Analytic solution of nonlinear singularly perturbed initial value problems through iteration ⋮ The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers ⋮ A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction-convection-diffusion equations ⋮ NIPG Method on Shishkin Mesh for Singularly Perturbed Convection–Diffusion Problem with Discontinuous Source Term ⋮ SDFEM with non-standard higher-order finite elements for a convection-diffusion problem with characteristic boundary layers ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ Supercloseness result of higher order FEM/LDG coupled method for solving singularly perturbed problem on S-type mesh ⋮ Superconvergence using pointwise interpolation in convection-diffusion problems ⋮ A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time ⋮ Convergence phenomena of \documentclass{article} \usepackage{amsmath,amsfonts}\pagestyle{empty}\begin{document} $\mathcal{Q}_p$ \end{document}‐elements for convection–diffusion problems ⋮ Error estimation in a balanced norm for a convection-diffusion problem with two different boundary layers ⋮ Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements ⋮ Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection-diffusion type ⋮ A painless multi-level automatic goal-oriented \(hp\)-adaptive coarsening strategy for elliptic and non-elliptic problems

Uses Software

• MooNMD
• UMFPACK

Cites Work

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• MooNMD -- a program package based on mapped finite element methods
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• Algorithm 832
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