Boundary collocation method vs fem for some harmonic 2-d problems

Abstract

The efficiency and computational accuracy of boundary collocation and finite element methods are compared. Two-dimensional harmonic boundary value problems are considered. The boundary collocation method is applied in the so-called straightforward version. Two families of the complete trial function sets are employed. In the finite element method also two types of finite elements are employed. The solutions for unknown functions are compared with exact solutions as functions of the mesh refinement. The conclusion which can be drawn from the numerical evidence is that for the same number of degrees of freedom the boundary collocation method results are more accurate than those obtained by finite element method. However, this advantage may be offset by the fact that the boundary collocation requires the solution to a set of linear algebraic equations with fully populated matrix of coefficients while the finite element method leads to a banded, and usually better conditioned, matrix.