Adaptive Galerkin Finite Element Methods for the Wave Equation

Abstract

AbstractThis paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the principle of \goaloriented" adaptivity which is based on a posteriori error estimation employing the solutions of auxiliary dual problems.