| Abstract: | The application of the finite element collocation method to two- and three-dimensional partial differential equations is hampered by the fact that its accuracy depends largely on the position of the collocation points. The method has, in the past, thus mainly been applied to two-dimensional differential equations defined on rectangular domains. In this case the method yields an optimal global convergence rate, when the Gauss-Legendre quadrature points are used as collocation points. It is shown in this paper that the same accuracy can also be achieved in the case of differential equations defined on nonrectangular domains. The only prerequisite for this is to solve the differential equation on a rectangular domain, mapped onto the nonrectangular domain of the differential equation by a bilinear blended map. © 1993 John Wiley & Sons, Inc. |
