Bespalov, Alexei; Heuer, Norbert Optimal error estimation for \(\mathbf {H}(\text{curl})\)-conforming \(p\)-interpolation in two dimensions. (English) Zbl 1203.65229 SIAM J. Numer. Anal. 47, No. 5, 3977-3989 (2009). 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. Reviewer: Nicolae Pop (Baia Mare) Cited in 3 Documents 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 Keywords:finite element method; \(p\)-interpolation; error estimation; Maxwell’s equations PDFBibTeX XMLCite \textit{A. Bespalov} and \textit{N. Heuer}, SIAM J. Numer. Anal. 47, No. 5, 3977--3989 (2009; Zbl 1203.65229) Full Text: DOI arXiv