A Convergence Analysis of an H-Version Finite Element Method with High Order Elements for Two Dimensional Elasto-Plasticity Problems.
MARYLAND UNIV COLLEGE PARK INST FOR PHYSICAL SCIENCE AND TECHNOLOGY
Pagination or Media Count:
In this paper, we will give an h-version finite element method for a two dimensional nonlinear elasto-plasticity problem. A family of admissible constitutive laws based on the so-called gauge function method is introduced first, and then a high order h-version semi-discretization scheme is presented . The existence and uniqueness of the solution for the semi-discrete problem are guaranteed by using some special properties of the constitutive law, and finally we will show that as the maximum element size h - 0 , the solution of the semi- discrete problem will converge to the solution of the continuous problem. The high order h-version discretization scheme introduced here is unusual. If the partition of the spatial space only has rectangles or parallelograms involved, then there would not be any limit on the element degree. However, if the partition of the spatial space has some triangular elements, then only certain combinations of finite element spaces for displacement and stress functions can be used. The discretization scheme also provides useful idea for applications of hp-version or high order h-version finite element methods for two dimensional problems where the elasto-plastic body is not a polygon, such as a disk or an annulus.
- Numerical Mathematics