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

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


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.


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


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© 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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