A C1-P2 finite element without nodal basis

Zhang, Shangyou

ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 2, pp. 175-192.

A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic equation. Numerical results are provided confirming the analysis.

Classification : 65N30, 73C35
Mots clés : differentiable finite element, quadratic element, biharmonic equation, Strang's conjecture, criss-cross grid, averaging interpolation, non-derivative basis

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