Numerical Analysis Group Research Report NA-96/23

Adaptive finite element methods for the damped wave equations

E. Süli and C. W. Wilkins

In this paper we derive a a posteriori error estimate in the L² and H^-1 norms for the damped wave equation. The proof of the error estimate is based on strong stability estimates of associated adjoint or dual problems, t ogether with the Galerkin orthogonality of the finite element method. Based on this a posteriori error estimate, we design an adaptive algorithm for determining both the spatial and temporal discretisation parameters so that we achieve global error control with respect to a prescribed tolerance. The performance of this numerical algorithm is demonstrated by some numerical experiments.