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A Posteriori Error Estimates for the Electric Field Integral Equation on Polyhedra

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Contributions to Partial Differential Equations and Applications

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 47))

Abstract

We present a residual-based a posteriori error estimate for the Electric Field Integral Equation (EFIE) on a bounded polyhedron \(\varOmega \) with boundary \(\varGamma \). The EFIE is a variational equation formulated in \({\varvec{H}^{-1/2}_{{{\mathrm{div}}}}(\varGamma )}\). We express the estimate in terms of \(L^2\)-computable quantities and derive global lower and upper bounds (up to oscillation terms).

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Ricardo H. Nochetto

  2. Mathematics Department, Center for Computational Engineering, RWTH Aachen University, Schinkelstr. 2, 52062, Aachen, Germany

    Benjamin Stamm

Authors
  1. Ricardo H. Nochetto
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  2. Benjamin Stamm
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Corresponding author

Correspondence to Benjamin Stamm .

Editor information

Editors and Affiliations

  1. Keldysh Institute of Applied Mathematics (IPM), Moscow, Russia

    B. N. Chetverushkin

  2. College of Technology, University of Houston, Houston, TX, USA

    W. Fitzgibbon

  3. Department of Mathematics, University of Houston, Houston, TX, USA

    Y.A. Kuznetsov

  4. Department of Mathematical Information, University of Jyväskylä, Jyväskylä, Finland

    P. Neittaanmäki

  5. University of Jyväskylä, Jyväskylä, Finland

    J. Periaux

  6. LJLL-UPMC, Paris, France

    O. Pironneau

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Nochetto, R.H., Stamm, B. (2019). A Posteriori Error Estimates for the Electric Field Integral Equation on Polyhedra. In: Chetverushkin, B., Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Periaux, J., Pironneau, O. (eds) Contributions to Partial Differential Equations and Applications. Computational Methods in Applied Sciences, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-78325-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-78325-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78324-6

  • Online ISBN: 978-3-319-78325-3

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