Paper Title
A Hybrid Method Based on Spectral Method and Finite Element Method for Second Order PDES

Solving PDEs in particular elliptic equations on closed and bounded regions is of great importance. In this article the spectral elements method for second order partial differential equations with dirichlet boundary conditions on regular region is considered. Although the main goal is to solve elliptic problems with this kind of boundary conditions, however, we present the method on general closed and bounded regions. At the end we compare the results of proposed method with the finite element methods. The numerical results shows the efficiency of our method. Index terms- Spectral Element Method, elliptic PDEs, Dirichlet boundary conditions, regular domains.