ADAPTIVE FINITE-ELEMENT METHODS FOR CONSERVATION-LAWS BASED ON A-POSTERIORI ERROR-ESTIMATES

We prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonality of the finite-element method. The strong stability estimate uses the entropy condition for the system in an essential way. (C) 1995 John Wiley & Sons, Inc.