Extrapolation and Related Techniques for Solving Ellipticequationsu

Extrapolation is a well-known numerical technique for raising the approximation order. Several variants of extrapolation can be used for elliptic partial diierential equations. The basic algorithmic variants are Richardson extrapolation, truncation error extrapolation and extrapolation of the functional. In multi-dimensional problems the error can be expanded into multivariate polynomials with respect to mesh parameters for the diierent coordinate directions. This can be exploited by multivariate extrapolation and the combination and sparse grid techniques. In this paper these methods are introduced and discussed in detail. The features and eeectiveness are illustrated in numerical experiments for model problems.