Minimizing some of the mesh errors in boundary element method

The discretization of the boundary in Boundary Element Method (BEM) requires several decisions that affect the accuracy of the BEM solution. These decisions include: the order of polynomial in each element, the continuity requirement at the element end, the location of the nodes inside the element, the size of the element, the location of the element end nodes, and the location of collocation points where the boundary conditions are imposed. The errors that are generated from these decisions are referred to as the mesh errors in this paper. In Ammons and Vable(1) the errors from continuity and collocation were discussed in detail and will not be considered here. But how to numerically determine an interpolation functions of a given order to satisfy a given continuity requirement will be discussed. The presentation will briefly describe three algorithms that minimize the L-1 norm of the mesh error from the remaining sources. These algorithms are applicable two-dimensional problems of Poisson's equation, Plate-Bending, Elastostatic, and Fracture mechanics formulated using direct or indirect BEM. Numerical examples will be presented showing the validity of these algorithms.