Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates

Details Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates

2011-09-15

arxiv.org/abs/1109.3259v1

Mathematics

Numerical Analysis

Scientific paper

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' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Affiliated with

Also associated with

No associations

Rating

Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-672417