Space-Time Finite Element Methods for Parabolic Evolution Problems with Non-smooth Solutions
Year: 2019
Type: preprint
Abstract: We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal parabolic regularity. We present new a priori estimates for low-regularity solutions. In order to avoid reduced convergence rates appearing in the case of uniform mesh refinement, we also consider adaptive refinement procedures based on residual a posteriori error indicators. The huge system of space-time finite element equations is then solved by means of GMRES preconditioned by algebraic multigrid.
Source: arXiv (Cornell University)
Authors: Langer, Ulrich, Schafelner, Andreas
Institution: Johannes Kepler University of Linz
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W2923116808