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Unified framework for an a posteriori error analysis of non-standard finite element approximations of H(curl)-elliptic problems. (English) Zbl 1196.65171

The authors provide a unified framework for an a posteriori error control of nonconforming finite element discretizations of \(H\)(curl)-elliptic problems as they arise from low-frequency electromagnetics:
\[ \text{curl}\,\,\mu^{-1}\text{curl}\,\, u+\sigma u=f \]
(in a bounded polyhedral domain). The idea governing this study is to rewrite the second-order partial differential equation as a system of two first-order in weak form. In particular, the interior penalty discontinuous Galerkin approach is presented.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
78A25 Electromagnetic theory (general)
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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