Adaptive Finite Element Method for 3D Problems

Special Research

Outline of the Project

The finite element method (FEM) is one of the most powerful numerical schemes that can be applied to the solution of physical problems, though there are still serious practical problems on FE mesh generation and its appropriate control, especially in three dimensional case. Mesh generation by hand is very time consuming and poor-quality meshes lead to unacceptable solutions. Adaptive finite element methods, in which quantitative control of FE errors is achieved automatically by finite element mesh regeneration based on posterior error estimation, were proposed in two dimensional cases some years ago. The purpose of our research is to extend these methods to three dimensional cases, which includes three subjects; 1)development of a full automatic mesh generator, 2) establishment of error estimation and mesh control, 3) application to various problems such as optimal deign problems, metal forming problems, elastic contact problems and so on.

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