Finite‐volume schemes for Friedrichs systems in multiple space dimensions: A priori and a posteriori error estimates

We consider a class of finite‐volume schemes on unstructured meshes for symmetric hyperbolic linear systems of balance laws in two and three space dimensions. This class of schemes has been introduced and analyzed by Vila and Villedieu ( 5 ). They have proven an a priori error estimate for approximations of smooth solutions. We extend the results to weak solutions. This is the base to derive an a posteriori error estimate for finite‐volume approximations of weak solutions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005