Nitsche-mortaring for singularly perturbed convection---diffusion problems

Authors:
Torsten Linβ;Hans-Görg Roos;Martin Schopf
Affiliations:
Institut für Numerische Mathematik, TU Dresden, Dresden, Germany 01062;Institut für Numerische Mathematik, TU Dresden, Dresden, Germany 01062;Institut für Numerische Mathematik, TU Dresden, Dresden, Germany 01062
Venue:
Advances in Computational Mathematics
Year:
2012

Citing 5
Cited 0

Anisotropic interpolation with applications to the finite element method

Computing
Superconvergence and the superconvergent patch recovery

Finite Elements in Analysis and Design - Special issue: Robert J. Melosh Medal Competition
A Multigrid Algorithm for the Mortar Finite Element Method

SIAM Journal on Numerical Analysis
Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems

Mathematics of Computation
The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the present paper we analyse a finite element method for a singularly perturbed convection---diffusion problem with exponential boundary layers. Using a mortaring technique we combine an anisotropic triangulation of the layer region (into rectangles) with a shape regular one of the remainder of the domain. This results in a possibly non-matching (and hybrid), but layer adapted mesh of Shishkin type. We study the error of the method allowing different asymptotic behaviour of the triangulations and prove uniform convergence and a supercloseness property of the method. Numerical results supporting our analysis are presented.