Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements

DOI10.1016/j.apnum.2011.02.001zbMath1213.65138OpenAlexW2171593034MaRDI QIDQ716057

Sebastian Franz, Gunar Matthies

Publication date: 19 April 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.02.001

zbMATH Keywords

convergencesingular perturbationerror estimatesnumerical examplesShishkin meshesconvection-diffusion problemGalerkin finite element methodboundary layersexponential layerscharacteristic layerslocal projection stabilization finite element method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability in context of PDEs (35B35) 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

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, SDFEM with non-standard higher-order finite elements for a convection-diffusion problem with characteristic boundary layers, Superconvergence using pointwise interpolation in convection-diffusion problems, Singularly perturbed reaction-diffusion problems as first order systems, A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time

Uses Software

• MooNMD
• UMFPACK

Cites Work

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