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Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws

Published online by Cambridge University Press:  15 April 2002

Christos Arvanitis ,
Theodoros Katsaounis  and
Charalambos Makridakis
Christos Arvanitis
Affiliation:
Department of Mathematics, University of Crete, Heraklion 71409, Greece. Institute for Applied and Computational Mathematics, FORTH, Heraklion 71110, Greece.
Theodoros Katsaounis
Affiliation:
Institute for Applied and Computational Mathematics, FORTH, Heraklion 71110, Greece. Department of Applied Mathematics, University of Crete, Heraklion 71409, Greece.
Charalambos Makridakis
Affiliation:
Institute for Applied and Computational Mathematics, FORTH, Heraklion 71110, Greece.
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Abstract

We propose and study semidiscrete and fully discretefinite element schemes based on appropriate relaxation models forsystems of Hyperbolic Conservation Laws.These schemes are using piecewise polynomials of arbitrary degree andtheir consistency error is of high order.The methods are combined with an adaptive strategy that yieldsfine mesh in shock regions and coarser mesh in the smooth parts of thesolution.The computational performance of these methods is demonstrated by considering scalar problems and the system of elastodynamics.

Keywords

Conservation lawsfinite elementsadaptive methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 1 , January 2001 , pp. 17 - 33
Copyright
© EDP Sciences, SMAI, 2001

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