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arXiv · 1903.02350

Space-Time Finite Element Methods for Parabolic Evolution Problems with Non-smooth Solutions

Ulrich Langer·Andreas Schafelner
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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.

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Ulrich Langer, Andreas Schafelner. 2019-03-06. Space-Time Finite Element Methods for Parabolic Evolution Problems with Non-smooth Solutions. https://arxiv.org/abs/1903.02350

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