Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem

Ljiljana Teofanov; Helena Zarin

doi:10.1007/s10543-009-0241-0

Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem

Ljiljana Teofanov, Helena Zarin

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Abstract

We consider a singularly perturbed elliptic problem with two small independent parameters and its discretization by a finite element method using piecewise bilinear elements on a layer-adapted mesh. We analyze superconvergence property of the method as well as a postprocessing technique which yields more accurate discrete solution. Numerical tests confirm our theoretical results.

Original language	English (US)
Pages (from-to)	743-765
Number of pages	23
Journal	BIT Numerical Mathematics
Volume	49
Issue number	4
DOIs	https://doi.org/10.1007/s10543-009-0241-0
State	Published - Nov 2009
Externally published	Yes

Bibliographical note

Funding Information:
This work was supported by the Ministry of Science and Technological Development of the Republic of Serbia under grant 144006.

Keywords

Finite element method
Layer-adapted mesh
Postprocessing
Singularly perturbed problems
Superconvergence
Two small parameters

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title = "Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem",

abstract = "We consider a singularly perturbed elliptic problem with two small independent parameters and its discretization by a finite element method using piecewise bilinear elements on a layer-adapted mesh. We analyze superconvergence property of the method as well as a postprocessing technique which yields more accurate discrete solution. Numerical tests confirm our theoretical results.",

keywords = "Finite element method, Layer-adapted mesh, Postprocessing, Singularly perturbed problems, Superconvergence, Two small parameters",

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AU - Teofanov, Ljiljana

AU - Zarin, Helena

N1 - Funding Information: This work was supported by the Ministry of Science and Technological Development of the Republic of Serbia under grant 144006.

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N2 - We consider a singularly perturbed elliptic problem with two small independent parameters and its discretization by a finite element method using piecewise bilinear elements on a layer-adapted mesh. We analyze superconvergence property of the method as well as a postprocessing technique which yields more accurate discrete solution. Numerical tests confirm our theoretical results.

AB - We consider a singularly perturbed elliptic problem with two small independent parameters and its discretization by a finite element method using piecewise bilinear elements on a layer-adapted mesh. We analyze superconvergence property of the method as well as a postprocessing technique which yields more accurate discrete solution. Numerical tests confirm our theoretical results.

KW - Finite element method

KW - Layer-adapted mesh

KW - Postprocessing

KW - Singularly perturbed problems

KW - Superconvergence

KW - Two small parameters

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Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem

Abstract

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Keywords

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