C1-Qk serendipity finite elements on rectangular meshes
Abstract
A C1-Qk serendipity finite element is a sub-element of C1-Qk BFS finite element such that the element remains C1-continuous and includes all Pk polynomials. In other words, it is a minimum of Qk bubbles enriched Pk finite element. We enrich the P4 and P5 spaces by 9 Q4 and 11 Q5-bubble functions, respectively. For all k 6, we enrich the Pk spaces exactly by 12 Qk bubble functions. We show the uni-solvence and quasi-optimality of the newly defined C1-Qk serendipity elements. Numerical experiments by the C1-Qk serendipity elements, 4 k 8, are performed.
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