Pointwise error estimates of the bilinear SDFEM on Shishkin meshes

Jin Zhang; Liquan Mei

doi:10.1002/num.21712

Pointwise error estimates of the bilinear SDFEM on Shishkin meshes

Jin Zhang
, Liquan Mei

School of Mathematics and Statistics

Xi'an Jiaotong University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 ε, with a pointwise accuracy of almost order 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results.

Original language	English
Pages (from-to)	422-440
Number of pages	19
Journal	Numerical Methods for Partial Differential Equations
Volume	29
Issue number	2
DOIs	https://doi.org/10.1002/num.21712
State	Published - Mar 2013

Keywords

SDFEM
Shishkin mesh
convection-diffusion
pointwise estimates
singular perturbation

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10.1002/num.21712

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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 ε, with a pointwise accuracy of almost order 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results.",

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AB - 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 ε, with a pointwise accuracy of almost order 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results.

KW - SDFEM

KW - Shishkin mesh

KW - convection-diffusion

KW - pointwise estimates

KW - singular perturbation

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DO - 10.1002/num.21712

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

Pointwise error estimates of the bilinear SDFEM on Shishkin meshes

Abstract

Keywords

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