This paper studies the asymptotic stability of traveling relaxation shock prooles for hyperbolic systems of conservation laws. Under a stability condition of subcharacteristic type the large time relaxation dynamics on the level of shocks is shown to be determined by the equilibrium conservation laws. The proof is due to the energy principle, using the weighted norms, the interaction of waves f...

We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing schemes, our approach updates model variables implementing two reconstructions alternately. First, Hermite interpolation reconstructs solution within cell matching point-based containing both physical values and their spatial derivatives. T...

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...

We discuss some recent developments and ideas in studying the compactness and asymptotic behavior of entropy solutions without locally bounded variation for nonlinear hyperbolic systems of conservation laws. Several classes of nonlinear hyperbolic systems with resonant or linear degeneracy are analyzed. The relation of the asymptotic problems to other topics such as scale-invariance, compactnes...

This paper describes a parallel algorithm based on discontinuous hp-finite element approximations of linear, scalar, hyperbolic conservation laws. The paper focuseson the development of an elTcctiveparallel adaptive strategy for such problems. Numerical experimeOlssuggest that these techniques are highly parallelizable and exponentially convergent, thereby yielding cflicien.:yIllany times super...