New development of the P and H-P version finite element method with quasi-uniform meshes for elliptic problems

In recent three decades, the finite element method (FEM) has rapidly developed as an important numerical method and used widely to solve large-scale scientific and engineering problems. In the fields of structural mechanics such as civil engineering, automobile industry and aerospace industry, the finite element method has successfully solved many engineering practical problems, and it has penetrated almost every field of today's sciences and engineering, such as material science, electricmagnetic fields, fluid dynamics, biology, etc. In this paper, we will overview and summarize the development of the p and h-p version finite element method, and introduce some recent new development and our newest research results of the p and h-p version finite element method with quasi-uniform meshes in three dimensions for elliptic problems.