The Mesh Transformation Method and Optimal Finite Element Solutions

Abstract

Since the accuracy of finite element solutions of partial differential equations is generally mesh dependent, especially when solutions have singularities and discontinuities, a proper mesh generation is often important and sometimes crucial for an accurate numerical approximation of such problems. In this paper, the mesh transformation method is applied to the boundary value problems of elliptic partial differential equations, and it is proved that the method leads to the optimal finite element solutions.