Coercive space-time finite element methods

Vortrag von Prof. Dr. Olaf Steinbach

Datum: 13.12.17  Zeit: 16.15 - 17.15  Raum: ETH HG E 1.2

For the numerical solution of time-dependent partial differential equations we consider space-time finite element methods which allow for an adaptive meshing simultaneously in space and time, and for a parallel solution of the global linear system. For the model problem of the heat equation we present a Galerkin--Petrov variational formulation where the test and ansatz spaces are of the same regularity. To prove the related stability condition we introduce and discuss a Hilbert type transformation operator. This concept is then also used to derive suitable variational formulations for the wave equation. Numerical results are given, and we will discuss future topics, challenges, and applications