On semiregular families of triangulations and linear interpolation. (English) Zbl 0728.41003

Summary: We consider triangulations formed by triangular elements. For the standard linear interpolation operator \(\pi_ h\) we prove the interpolation order to be \(\| v-\pi_ hv\|_{1,p}\leq Ch| v|_{2,p}\) for \(p>1\) provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal’s condition upon the minimum angle need not be satisfied.


41A05 Interpolation in approximation theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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