A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

Gabriel Barrenechea, John Volker, Petr Knobloch

Research output: Contribution to journalArticle

Abstract

An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steadystate and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.
LanguageEnglish
Pages1335-1366
Number of pages32
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume47
Issue number5
Early online date13 Mar 2013
DOIs
Publication statusPublished - 30 Jul 2013

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Convection-diffusion-reaction Equation
Nonlinear Diffusion
Stabilization
Finite Element Method
Projection
Finite element method
Oscillation
Error Estimates
Numerical Study
Uniqueness
Term
Demonstrate
Convection

Keywords

  • finite element method
  • local projection stabilization
  • crosswind diffusion
  • convection-diffusion-reaction equation
  • well posedness
  • time dependent problem
  • stability
  • error estimate

Cite this

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abstract = "An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steadystate and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.",
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AU - Knobloch, Petr

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N2 - An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steadystate and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.

AB - An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steadystate and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.

KW - finite element method

KW - local projection stabilization

KW - crosswind diffusion

KW - convection-diffusion-reaction equation

KW - well posedness

KW - time dependent problem

KW - stability

KW - error estimate

U2 - 10.1051/m2an/2013071

DO - 10.1051/m2an/2013071

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JO - ESAIM: Mathematical Modelling and Numerical Analysis

T2 - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

SN - 0764-583X

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ER -