FV upwind stabilization of FE discretizations for advection-diffusion problems

Brunner F, Frank F, Knabner P (2014)

Publication Status: Published

Publication Type: Conference contribution, Conference Contribution

Publication year: 2014

Publisher: Springer New York LLC

Book Volume: 77

Pages Range: 177-185

Conference Proceedings Title: Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Event location: Berlin DE

ISBN: 9783319056838

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_BrunnerFrankKn_FVUpwindStabOfFEForAdvancedDiffProblems

DOI: 10.1007/978-3-319-05684-5_16

Abstract

We apply a novel upwind stabilization of a mixed hybrid finite element method of lowest order to advection–diffusion problemswith dominant advection and compare it with a finite element scheme stabilized by finite volume upwinding. Both schemes are locally mass conservative and employ an upwind-weighting formula in the discretization of the advective term. Numerical experiments indicate that the upwind-mixed method is competitive with the finite volume method. It prevents the appearance of spurious oscillations and produces nonnegative solutions for strongly advection-dominated problems, while the amount of artificial diffusion is lower than that of the finite volume method. This makes the method attractive for applications in which too much numerical diffusion is critical and may lead to false predictions; e.g., if highly nonlinear reactive processes take place only in thin interaction regions.

Authors with CRIS profile

Fabian Brunner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Florian Frank Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Brunner, F., Frank, F., & Knabner, P. (2014). FV upwind stabilization of FE discretizations for advection-diffusion problems. In Fuhrmann Jürgen, Ohlberger Mario, Rohde Christian (Eds.), Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects (pp. 177-185). Berlin, DE: Springer New York LLC.

MLA:

Brunner, Fabian, Florian Frank, and Peter Knabner. "FV upwind stabilization of FE discretizations for advection-diffusion problems." Proceedings of the 7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7, Berlin Ed. Fuhrmann Jürgen, Ohlberger Mario, Rohde Christian, Springer New York LLC, 2014. 177-185.

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