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

We develop and analyze an adaptive hybridized Interior PenaltyDiscontinuous Galerkin (IPDG-H) method for H(curl)-ellipticboundary value problems in 2D or 3D arising from asemi-discretization of the eddy currents equations. The method canbe derived from a mixed formulation of the given boundary valueproblem and involves a Lagrange multiplier that is an approximationof the tangential traces of the primal variable on the interfaces ofthe underlying triangulation of the computational domain. It isshown that the IPDG-H technique can be equivalently formulated andthus implemented as a mortar method. The mesh adaptation is based ona residual-type a posteriori error estimator consisting of elementand face residuals. Within a unified framework for adaptive finiteelement methods, we prove the reliability of the estimator up to aconsistency error. The performance of the adaptive symmetric IPDG-Hmethod is documented by numerical results for representative testexamples in 2D.