The Boundary Element Method for Non-Linear Problems

This work is concerned with the analysis of material non-linear problems with the boundary element method (BEM).

For solving such problems, a domain discretisation is required in addition to the boundary discretisation, and therefore, internal cells are used. Because of this, an additional discretisation error, which affects the quality of the results, is introduced. The aim of this work is to adaptively control this discretisation error.

A new method for an adaptive error-controlled cell-refinement is presented. The error introduced by the cell size is estimated and on the basis of the error indicator, the cell mesh is automatically refined.

The main contribution of this work is towards an efficient and accurate evaluation of the domain integrals and an adaptive refinement procedure with non-conforming cell meshes. In addition, existing criteria for determining the number of integration points are reviewed and new integration criteria are developed.

The algorithm which is implemented is valid for two- and three-dimensional prob-lems. The high accuracy of this new method is verified by numerical examples.