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A C1-P2 finite element without nodal basis. (English) Zbl 1145.65102
The author introduces a new finite element, which is continuously differentiable, but consists only of piecewise quadratic polynomials on a type of uniform triangulations and constructs a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, the author has to construct a special averaging operator which is stable and preserves quadratic polynomials. He obtains the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic equation. Numerical results are provided confirming the analysis.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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