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Triangular finite elements of HCT type and class \(C^ \rho\). (English) Zbl 0832.65003
Let \(\tau\) be some triangulation of a bounded polygonal domain \(\Omega \subset\mathbb{R}^2\). Let \(\tau_3\) be the Hsieh-Clough-Tocher (HCT) subtriangulation of \(\tau\) obtained by joining an interior point of each triangle to its vertices. For a smooth function \(u\), the authors construct a piecewise polynomial function \(v \in C^\rho (\Omega)\) of degree \(n = 3\rho\) for \(\rho\) odd and \(n = 3\rho + 1\) for \(\rho\) even, on the subtriangulation \(\tau_3\); the function \(v\) interpolates the derivatives of \(u\) up to order \(\rho\) at the vertices of \(\tau\).

65D05 Numerical interpolation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A05 Interpolation in approximation theory
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
Full Text: DOI
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