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Energy-Corrected Finite Element Methods for Scalar Elliptic Problems

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Numerical Mathematics and Advanced Applications - ENUMATH 2013

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

In this work, we consider the finite element solution of several scalar elliptic problems with singularities in two dimensions.We outline recent theoretical developments in energy corrected approaches and demonstrate numerically that by local and easy to implement modifications of the discrete operators, optimal convergence orders in weighted Sobolev norms can be recovered.

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Authors and Affiliations

  1. Institute for Numerical Mathematics, Technische Universität München, Boltzmannstraße 3, 85748, Garching b. München, Germany

    Thomas Horger, Christia Waluga & Barbara Wohlmuth

  2. Universität Erlangen-Nürnberg, Lehrstuhl für Informatik 10, Cauerstraße 11, 91058, Erlangen, Germany

    Markus Huber & Ulrich Rüde

Authors
  1. Thomas Horger
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  2. Markus Huber
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  3. Ulrich Rüde
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  4. Christia Waluga
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  5. Barbara Wohlmuth
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Corresponding author

Correspondence to Christia Waluga .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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© 2015 Springer International Publishing Switzerland

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Cite this paper

Horger, T., Huber, M., Rüde, U., Waluga, C., Wohlmuth, B. (2015). Energy-Corrected Finite Element Methods for Scalar Elliptic Problems. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_2

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