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Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. (English) Zbl 1063.78021
Summary: We develop the a posteriori error estimation of mixed discontinuous Galerkin finite element approximations of the Maxwell operator. In particular, by employing suitable Helmholtz decompositions of the error, together with the conservation properties of the underlying method, computable upper bounds on the error, measured in terms of a natural (mesh-dependent) energy norm, are derived. Numerical experiments testing the performance of our a posteriori error bounds for problems with both smooth and singular analytical solutions are presented.

MSC:
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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