Polygonal Finite Element Method For Planar Elasticity Problems

The main content of this paper is to study the polygonal finite element method for plane elasticity problems,to conduct the error analysis,and to examine the locking phenomenon both theoretically and numerically.Firstly,we introduce the model problem,its finite element dis-cretization,and the generalized barycentric coordinates.With the aid of the generalized barycentric coordinates on arbitrary convex polygons,we construct a polygonal conforming finite element method for elasticity problems.Then we prove the convergence rate of this method,and analyze its locking phenomenon.Finally,numerical re-sults are presented.