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Quadratic serendipity finite elements on polygons using generalized barycentric coordinates
2014
Mathematics of Computation
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity'
doi:10.1090/s0025-5718-2014-02807-x
fatcat:uz26lzmadrhdlev6ygzxy6z3vy