Volume 4, Issue 1
Adaptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems

C. Carstensen, R. H. W. Hoppe, N. Sharma & T. Warburton

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 13-37.

Published online: 2011-04

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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

Adaptive hybridized Interior Penalty Discontinuous Galerkin method, a posteriori error analysis, H(curl)-elliptic boundary value problems, semi-discrete eddy currents equations.

  • AMS Subject Headings

65N30, 65N50, 78M10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-13, author = {}, title = {Adaptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {1}, pages = {13--37}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1007}, url = {http://global-sci.org/intro/article_detail/nmtma/5956.html} }
TY - JOUR T1 - Adaptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 13 EP - 37 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1007 UR - https://global-sci.org/intro/article_detail/nmtma/5956.html KW - Adaptive hybridized Interior Penalty Discontinuous Galerkin method, a posteriori error analysis, H(curl)-elliptic boundary value problems, semi-discrete eddy currents equations. AB -

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.

C. Carstensen, R. H. W. Hoppe, N. Sharma & T. Warburton. (2020). Adaptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems. Numerical Mathematics: Theory, Methods and Applications. 4 (1). 13-37. doi:10.4208/nmtma.2011.m1007
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