Pointwise estimates of the SDFEM for convection-diffusion problems with characteristic layers

Authors:
Jin Zhang;Liquan Mei;Yaping Chen
Affiliations:
School of Science, Xian Jiaotong University, Xian, 710049, China;School of Science, Xian Jiaotong University, Xian, 710049, China;School of Science, Xian Jiaotong University, Xian, 710049, China
Venue:
Applied Numerical Mathematics
Year:
2013

Citing 5
Cited 0

Anisotropic interpolation with applications to the finite element method

Computing
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
Solving unsymmetric sparse systems of linear equations with PARDISO

Future Generation Computer Systems - Special issue: Selected numerical algorithms
Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

A model singularly perturbed convection-diffusion problem in two space dimensions is considered. The problem is solved by a streamline diffusion finite element method (SDFEM) that uses piecewise bilinear finite elements on a Shishkin mesh. We prove that the method is convergent, independently of the diffusion parameter @e, with a pointwise accuracy of almost order 7/4 away from the characteristic layers. Numerical experiments support these theoretical results.