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strang's conjecture

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A C1-P2 finite element without nodal basis
Shangyou Zhang
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 42 / Issue 2 / March 2008

Published online by Cambridge University Press:

27 March 2008, pp. 175-192

Print publication:

March 2008
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 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.