Convergence phenomena of \documentclass{article} \usepackage{amsmath,amsfonts}\pagestyle{empty}\begin{document} $\mathcal{Q}_p$ \end{document}‐elements for convection–diffusion problems

DOI10.1002/num.21709zbMath1255.65211OpenAlexW2118767667MaRDI QIDQ4903220

Sebastian Franz

Publication date: 21 January 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21709

zbMATH Keywords

singular perturbationsuperconvergenceboundary layerslayer-adapted meshes

Mathematics Subject Classification ID

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

Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: vertex-cell interpolation ⋮ 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

Uses Software

• MooNMD

Cites Work

• Corner singularities and boundary layers in a simple convection-diffusion problem
• Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems
• SDFEM with non-standard higher-order finite elements for a convection-diffusion problem with characteristic boundary layers
• MooNMD -- a program package based on mapped finite element methods
• Using rectangularqpelements in the SDFEM for a convection-diffusion problem with a boundary layer
• Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers
• Local projection stabilisation on \(S\)-type meshes for convection-diffusion problems with characteristic layers
• Layer-adapted meshes for reaction-convection-diffusion problems
• Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem
• Analysis of a new stabilized higher order finite element method for advection-diffusion equations
• Finite Element Methods for Navier-Stokes Equations
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
• Uniform superconvergence of a Galerkin finite element method on Shishkin-type meshes
• Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems
• Superconvergence analysis of the Galerkin FEM for a singularly perturbed convection–diffusion problem with characteristic layers
• A note on the conditioning of upwind schemes on Shishkin meshes
• Numerical methods on Shishkin meshes for linear convection-diffusion problems
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
• Unnamed Item
• Unnamed Item