Contributed Talk
A posteriori error estimation for high-order time discretisations of parabolic equations
Torsten Linss, FernUniversität in Hagen, Germany,
FernUniversität in Hagen, Germany
Abstract
Time-stepping procedures of arbitrary order and flavour (extrapolation, discontinuous and continuous Galerkin methods, BDF, ...) are considered for the discretisation of parabolic initial-boundary value problems. They are combined with finite element discretisations in space. We aim at deriving a posteriori error bounds in the maximum norm. Our analysis relys on derivative bounds for the Green's function associated with the parabolic operator, the availability of a posteriori error bounds for the elliptic problem and on suitable polynomial reconstructions of approximations given at certain points in time only. The talk will focus on the latter.
This is joint work with Martin Ossadnik (FernUni in Hagen) and Goran Radojev (University of Novi Sad)