A coercive space time finite element method for parabolic problems

Univ.-Prof. Dr. Olaf Steinbach

June 13, 2017, 11:45 a.m. S2 059

Space-time finite and boundary element methods are meanwhile well established for the numerical solution of time-dependent partial differential equations. In particular for the heat equation it can be shown that related boundary integral operators are elliptic in anisotropic Sobolev spaces, while unique solvability of domain variational formulations is based on suitable stability conditions in Bochner spaces. This mismatch is due to a different handling of the time derivative. Hence we discuss variational formulations of the first order time derivative which turs out to be coercive, and which even allows for a symmetric discretization. Moreover, this approach allows to recover ellipticity estimates for boundary integral operators.