Journal paper in Mathematics for Computation

Journal paper accepted for publication in Mathematics for Computation, 2013

A. Rand; A. Gillette; C. Bajaj
Quadratic Serendipity Finite Elememts on Polygons using Genralized Barycentric Coordinates
Mathematics for Computation, Accepted for Publication, 2013.

Abstract:
We introduce a nite 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, 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’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori
error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity
constructions, and applications to adaptive meshing are discussed.

Manuscript can be found from full list of publications

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