A nonlinear local projection stabilization for convection-diffusion-reaction equations

Gabriel Barrenechea, Volker John, Petr Knobloch

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Abstract

We propose a new local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations. The discretization contains a crosswind diffusion term which depends on the unknown discrete solution in a nonlinear way. Consequently, the resulting method is nonlinear. Solvability of the nonlinear problem is established and an a priori error estimate in the LPS norm is proved. Numerical results show that the nonlinear crosswind diffusion term leads to a reduction of spurious oscillations.
Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications 2011
Subtitle of host publicationProceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011
EditorsA. Cangiani, R. L. Davidchack, E. H. Georgoulis, A. N. Gorban, J. Levesley, M. V. Tretyakov
PublisherSpringer-Verlag
Pages237-245
Number of pages9
ISBN (Electronic)9783642331343
ISBN (Print)9783642331336, 9783662511299
DOIs
Publication statusPublished - 10 Sep 2012
EventENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications - University of Leicester, Leicester , United Kingdom
Duration: 5 Sep 20119 Sep 2011

Conference

ConferenceENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications
Abbreviated titleENUMATH 2011
Country/TerritoryUnited Kingdom
CityLeicester
Period5/09/119/09/11

Keywords

  • numerical techniques
  • efficient computational techniques

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