Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes
Abstract
We extend the C1-P3 Fraeijs de Veubeke-Sander finite element to two families of C1-Pk (k>3) macro finite elements on general quadrilateral meshes. On each quadrilateral, four Pk polynomials are defined on the four triangles subdivided from the quadrilateral by its two diagonal lines. The first family of C1-Pk finite elements is the full C1-Pk space on the macro-mesh. Thus the element can be applied to interface problems. The second family of C1-Pk finite elements condenses all internal degrees of freedom by moving them to the four edges. Thus the second element method has much less unknowns but is more accurate than the first one. We prove the uni-solvency and the optimal order convergence. Numerical tests and comparisons with the C1-Pk Argyris are provided.
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