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Approximation by quadrilateral finite elements. (English) Zbl 0993.65125
This paper concerns the approximation properties of finite element spaces on quadilateral meshes. The finite element spaces are constructed starting with a finite-dimensional space of functions on a square reference element, which is then transformed to a space of functions on each convex quadrilateral element via a bilinear isomorphism on the space onto the element. It is demonstrated the degradation of the convergence order on quadrilateral meshes as compared to triangular meshes for serendipity finite elements and for various mixed and nonconforming finite elements.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A27 Inverse theorems in approximation theory
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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References:
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