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

Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2013) A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis, 47 (5). pp. 1335-1366. ISSN 0764-583X (https://doi.org/10.1051/m2an/2013071)

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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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• Item metadata

  Item type:	Article
  ID code:	44162
  Dates:	Date Event 30 July 2013 Published 13 March 2013 Published Online
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	20 Jun 2013 08:44
  Last modified:	08 Apr 2024 20:35
  URI:	https://strathprints.strath.ac.uk/id/eprint/44162