Finite element solution to the second order elliptic problems

摘要

In this paper we develop some fundamental results of vector calculus in the barycentric coordinate system and apply it to the finite element solution of the second order elliptic boundary value problems. Several numerical quadratures for the boundary value problems in this coordinate system are derived and some numerical experiments for the solution of the Poisson equation in a triangular domain with inhomogeneous boundary condition are provided.