Sobotíková, V. Finite elements on curved domains. (English) Zbl 0933.65132 East-West J. Numer. Math. 4, No. 2, 137-149 (1996). Summary: The use of curved elements in the finie element method in case of nonpolygonal domains is examined. Several modifications of classical linear elements are introduced and their relations and approximation properties are studied. The generalization of M. Zlámal’s ideal interpolation theory [SIAM J. Numer. Anal. 10, 229-240 (1973; Zbl 0285.65067)] to the spaces \(W^{1,p}\), \(p\geq 1\), is presented. Cited in 1 Document MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N15 Error bounds for boundary value problems involving PDEs 41A63 Multidimensional problems 65D05 Numerical interpolation Keywords:ideal interpolation; natural extension; error estimates; curved elements; finie element method Citations:Zbl 0285.65067 PDFBibTeX XMLCite \textit{V. Sobotíková}, East-West J. Numer. Math. 4, No. 2, 137--149 (1996; Zbl 0933.65132)