Adaptive finite element relaxation schemes for hyperbolic conservation laws

We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservat ion Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined wit h an adaptive strategy that yields fine mesh in shock regions and coarser m esh in the smooth parts of the solution. The computational performance of t hese methods is demonstrated by considering scalar problems and the system of elastodynamics.