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

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Large-Scale Scientific Computing (LSSC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11958))

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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 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.

Supported by the Austrian Science Fund under the grant W1214, project DK4.

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Notes

  1. 1.

    http://mfem.org/.

  2. 2.

    https://www.llnl.gov/casc/hypre/.

  3. 3.

    https://www.ricam.oeaw.ac.at/hpc/.

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Author information

Authors and Affiliations

  1. Institute for Computational Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria

    Ulrich Langer

  2. Doctoral Program “Computational Mathematics”, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria

    Andreas Schafelner

Authors
  1. Ulrich Langer
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  2. Andreas Schafelner
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Corresponding author

Correspondence to Ulrich Langer .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Langer, U., Schafelner, A. (2020). Space-Time Finite Element Methods for Parabolic Initial-Boundary Value Problems with Non-smooth Solutions. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science(), vol 11958. Springer, Cham. https://doi.org/10.1007/978-3-030-41032-2_68

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  • DOI: https://doi.org/10.1007/978-3-030-41032-2_68

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41031-5

  • Online ISBN: 978-3-030-41032-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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