A Posteriori Error Analysis And Adaptivity For Finite Element Approximations Of Hyperbolic Problems

A posteriori error analysis and adaptivity for nite element approximations of hyperbolic problems a Endre S uli The aim of this article is to present an overview of recent developments in the area of a posteriori error estimation for nite element approximations of hyperbolic problems. The approach pursued here rests on the systematic use of hyperbolic duality arguments. We also discuss the question of computational implementation of the a posteriori error bounds into adaptive nite element algorithms. Warnecke for helpful discussions on various aspects of a posteriori error analysis and adaptivity. I am particularly indebted to my colleague Paul Houston for performing the numerical experiments which appear in this paper. a This work was presented in a lecture series at the International School on Conservation Laws in Freiburg, Germany, October 1997: I wish to express my gratitude to Dietmar Krr oner for his kind hospitality.