We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar problems and the system of elastodynamics.
@article{M2AN_2001__35_1_17_0,
author = {Arvanitis, Christos and Katsaounis, Theodoros and Makridakis, Charalambos},
title = {Adaptive finite element relaxation schemes for hyperbolic conservation laws},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {35},
year = {2001},
pages = {17-33},
mrnumber = {1811979},
zbl = {0980.65104},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2001__35_1_17_0}
}
Arvanitis, Christos; Katsaounis, Theodoros; Makridakis, Charalambos. Adaptive finite element relaxation schemes for hyperbolic conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 17-33. http://gdmltest.u-ga.fr/item/M2AN_2001__35_1_17_0/
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