An elliptic singularly perturbed problem with two parameters II: Robust finite element solution

Authors:
Lj. Teofanov;H. -G. Roos
Affiliations:
Department for Fundamental Disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg D.Obradovića 6, 21000 Novi Sad, Serbia;Institute of Numerical Mathematics, Technical University of Dresden, Dresden D-01062, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 6
Cited 1

Solution of a boundary value problem for an elliptic equation with a small parameter for the leading derivatives

USSR Computational Mathematics and Mathematical Physics
Anisotropic interpolation with applications to the finite element method

Computing
A higher-order scheme for quasilinear boundary value problems with two small parameters

Computing
Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems

Mathematics of Computation
A parameter robust second order numerical method for a singularly perturbed two-parameter problem

Applied Numerical Mathematics
An elliptic singularly perturbed problem with two parameters I: Solution decomposition

Journal of Computational and Applied Mathematics

A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem

Advances in Computational Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper we consider a singularly perturbed elliptic model problem with two small parameters posed on the unit square. The problem is solved numerically by the finite element method using piecewise linear or bilinear elements on a layer-adapted Shishkin mesh. We prove that method with bilinear elements is uniformly convergent in an energy norm. Numerical results confirm our theoretical analysis.