A coercive space time finite element method for parabolic problems

Univ.-Prof. Dr. Olaf Steinbach

June 13, 2017, 1:45 p.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.