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Adaptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems

Published online by Cambridge University Press:  28 May 2015

C. Carstensen ,
R. H. W. Hoppe ,
N. Sharma  and
T. Warburton
C. Carstensen
Affiliation:
Department of Mathematics, Humboldt Universität zu Berlin, D-10099 Berlin, Germany Department of Computer Science Engineering, Yonsei University, Seoul 120-749, Korea
R. H. W. Hoppe
Affiliation:
Department of Mathematics, University of Houston, Houston TX 77204-3008, USA Institute of Mathematics, University of Augsburg, D-86159 Augsburg, Germany
N. Sharma
Affiliation:
Department of Mathematics, University of Houston, Houston TX 77204-3008, USA
T. Warburton
Affiliation:
CAAM, Rice University, Houston, TX 77005-1892, USA
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Abstract

We develop and analyze an adaptive hybridized Interior Penalty Discontinuous Galerkin (IPDG-H) method for H(curl)-elliptic boundary value problems in 2D or 3D arising from a semi-discretization of the eddy currents equations. The method can be derived from a mixed formulation of the given boundary value problem and involves a Lagrange multiplier that is an approximation of the tangential traces of the primal variable on the interfaces of the underlying triangulation of the computational domain. It is shown that the IPDG-H technique can be equivalently formulated and thus implemented as a mortar method. The mesh adaptation is based on a residual-type a posteriori error estimator consisting of element and face residuals. Within a unified framework for adaptive finite element methods, we prove the reliability of the estimator up to a consistency error. The performance of the adaptive symmetric IPDG-H method is documented by numerical results for representative test examples in 2D.

Keywords

65N3065N5078M10Adaptive hybridized Interior Penalty Discontinuous Galerkin methoda posteriori error analysisH(curl)-elliptic boundary value problemssemi-discrete eddy currents equations
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 1 , February 2011 , pp. 13 - 37
Copyright
Copyright © Global Science Press Limited 2011

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