Numerical solving of singularly perturbed boundary value problems with discontinuities

Helena Zarin; Snezana Gordič

Numerical solving of singularly perturbed boundary value problems with discontinuities

Helena Zarin, Snezana Gordič

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

Abstract

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the "-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to stabilize Galerkin FEM and prove "-uniform convergence of the second order.

Original language	English (US)
Pages (from-to)	131-145
Number of pages	15
Journal	Novi Sad Journal of Mathematics
Volume	42
Issue number	1
State	Published - Jul 25 2012
Externally published	Yes

Keywords

Convection-diffusion
Layer-adapted mesh
Standard Galerkin method
Streamline-diffusion finite element method

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abstract = "One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the {"}-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to stabilize Galerkin FEM and prove {"}-uniform convergence of the second order.",

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author = "Helena Zarin and Snezana Gordi{\v c}",

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T1 - Numerical solving of singularly perturbed boundary value problems with discontinuities

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AU - Gordič, Snezana

PY - 2012/7/25

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N2 - One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the "-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to stabilize Galerkin FEM and prove "-uniform convergence of the second order.

AB - One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the "-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to stabilize Galerkin FEM and prove "-uniform convergence of the second order.

KW - Convection-diffusion

KW - Layer-adapted mesh

KW - Standard Galerkin method

KW - Streamline-diffusion finite element method

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JF - Novi Sad Journal of Mathematics

IS - 1

ER -

Numerical solving of singularly perturbed boundary value problems with discontinuities

Abstract

Keywords

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