Orthogonal collocation in the nonconforming boundary element method

Abstract

This paper outlines the use of non-conforming (discontinuous) elements in the collocation boundary element method for solving two-dimensional potential and Poisson type problems. The roots of an orthogonal polynomial (shifted Jacobi polynomial) are used as the collocation points. This results in increased accuracy due to the least square minimization property of the orthogonal polynomials. The advantage of using non-conforming elements is realized when the method is applied (i) to problems with singularities (both due to geometry and boundary conditions) and (ii) in conjunction with domain decomposition techniques. Also, the collocation points can be relocated within an element by changing two user-defined parameters in the shifted Jacobi polynomial, thus providing an error indicator which can be used for mesh refinement purposes. This technique, called the rh method, is discussed and illustrated. The results obtained by using non-conforming boundary elements for standard test problems are shown to be accurate.