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Optimal error estimation for \(\mathbf {H}(\text{curl})\)-conforming \(p\)-interpolation in two dimensions. (English) Zbl 1203.65229

The main result of the paper is an optimal estimate for an \(\mathbf{H}(\text{curl})\)-conforming projection based \(p\)-interpolation operator \(\Pi_p^{\text{curl}}\). For the proof, the authors, uses a regular splitting of \(\mathbf{u}\in \mathbf{H}^r(\text{curl}, K)\) into a curl-free component and a complementary vector field of extra smoothness.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
35Q61 Maxwell equations
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