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Space-Time Finite Element Methods for Parabolic Initial-Boundary Value Problems with Non-smooth Solutions

  • Ulrich LangerEmail author
  • Andreas Schafelner
Conference paper
  • 55 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

We propose consistent, locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems under the assumption of maximal parabolic regularity. We present new a priori discretization error estimates for low-regularity solutions, and some numerical results including results for an adaptive version of the scheme and strong scaling results.

Keywords

Parabolic initial-boundary-value problems Space-time finite element methods Unstructured meshes Adaptivity 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute for Computational MathematicsJohannes Kepler University LinzLinzAustria
  2. 2.Doctoral Program “Computational Mathematics”, Johannes Kepler University LinzLinzAustria

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