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An a posteriori error indicator for discontinuous Galerkin discretizations of $$H$$(curl)-elliptic partial differential equations. (English) Zbl 1148.65088
Summary: We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of $$H(\text{curl}; \Omega)$$-elliptic boundary value problems that arise in eddy current models. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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