@Article{NMTMA-4-13,
author = {C. Carstensen, R. H. W. Hoppe, N. Sharma and T. Warburton},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.m1007},
url = {http://global-sci.org/intro/article_detail/nmtma/5956.html}
}