A C1-P2 finite element without nodal basis

Shangyou Zhang
2008 Mathematical Modelling and Numerical Analysis  
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
more » ... ng the biharmonic equation. Numerical results are provided confirming the analysis. Mathematics Subject Classification. 65N30, 73C35.
doi:10.1051/m2an:2008002 fatcat:3qomjmutgjazvmyesizq36mv7m