Locally stabilized space-time finite element methods on anisotropic hexahedral decompositions
Andreas SchafelnerNov. 24, 2020, 2:30 p.m. ZOOM
We present locally stabilized, conforming space-time finite element methods for parabolic evolution equations on hexahedral decompositions of the space-time cylinder. Tensor-product decompositions allow for anisotropic a priori error estimates, that are explicit in spatial and temporal meshsizes. Moreover, tensor-product finite elements are suitable for anisotropic adaptive mesh refinement strategies provided that an appropriate a posteriori discretization error estimator is available. The large-scale system of space-time finite element equations is then solved by means of the Flexible Generalized Minimal Residual (FGMRES)method preconditioned by space-time algebraic multigrid. We present and discuss numerical results for several examples possessing different features.
This work was supported by the Austrian Science Fund (FWF) under grant W1214, project DK4.