SDFEM with non-standard higher-order finite elements for a convection-diffusion problem with characteristic boundary layers

DOI10.1007/s10543-010-0307-zzbMath1230.65116OpenAlexW1976654029MaRDI QIDQ639956

Sebastian Franz

Publication date: 11 October 2011

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0307-z

zbMATH Keywords

convergencesingular perturbationconvection-diffusion problemShishkin meshhigher-order finite elementscharacteristic boundary layersexponential layersstreamline diffusion finite element method (SDFEM)

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 (9)

Iterative analytic approximation to nonlinear convection dominated systems ⋮ 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 ⋮ Physics-informed neural networks with parameter asymptotic strategy for learning singularly perturbed convection-dominated problem ⋮ Superconvergence using pointwise interpolation in convection-diffusion problems ⋮ 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 ⋮ Crank-Nicolson leap-frog time stepping decoupled scheme for the fluid-fluid interaction problems ⋮ Local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems

Cites Work

• Unnamed Item
• Unnamed Item
• Corner singularities and boundary layers in a simple convection-diffusion problem
• Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems
• Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements
• 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
• Continuous interior penalty method on a Shishkin mesh for convection-diffusion problems with characteristic boundary layers
• A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem
• 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
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• 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
• The optimization of methods of solving boundary value problems with a boundary layer
• Numerical methods on Shishkin meshes for linear convection-diffusion problems

This page was built for publication: SDFEM with non-standard higher-order finite elements for a convection-diffusion problem with characteristic boundary layers