Finite volume schemes for hyperbolic-parabolic systems : error estimates
Finite-volume schemes on unstructured grids are the most frequently used to approximate solutions of systems of hyperbolic balance laws in multi-space dimension. The convergence analysis for the scalar case is well developed, even though not complete up to now. In contrast, very few is known for the case of systems. Following the ideas of J.P. Vila and P. Villedieu on one side, and of C.Dafermos on the other side, we derive error estimates of the order $O(h^{1/2})$ for finite volume schemes to some hyperbolic--parabolic systems in multi-space dimension. This includes in particular the Euler system with a source term, the compressible Navier--Stokes system and the Friedrichs' system. The error estimates are valid for smooth solutions. In addition, in the case of the Friedrichs' system they hold also for solutions with jumps.
Finite Volumen Verfahren, Navier-Stokes System, Finite Volume Schemes, Balance Laws
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