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A rational interpolation scheme on a quadrilateral from the class \(C^2\). (Un schéma d’interpolation rationnel sur un quadrilatère de classe \(C^2\).) (French) Zbl 0974.65013
Let \(\Omega\) be a planar polygonal domain. By using a partition of \(\Omega\) into convex quadrilaterals, the author constructs for each function \(f\in C^2(\Omega)\) a function \(\pi f\in C^2(\Omega)\) that interpolates position values and derivatives of \(f\) at the vertices of the quadrilaterals. The restriction of \(\pi f\) on each quadrilateral is the sum of a finite element, obtained from a polynomial scheme of FVS type, and a certain rational function.

MSC:
65D05 Numerical interpolation
41A20 Approximation by rational functions
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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