Adaptive Finite Element Methods for Conservation Laws Based on a Posteriori ErrorEstimates

摘要

We prove a posteriori error estimates for a finite element method for systems ofstrictly 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.