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Residual based a posteriori error estimators for eddy current computation. (English) Zbl 0949.65113
From the authors’ abstract: We consider \(H (\text{curl};\Omega)\)-elliptic problems that have been discretized by means of Nedelec’s edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive mesh refinement. The fundamental tool in the analysis is a Helmholtz-type decomposition of the error into an irrotational part and a weakly solenoidal part.

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A55 Technical applications of optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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