Integration-free Coons macroelements for the solution of 2D Poisson problems

摘要

Large isoparametric macroelements with closed-form cardinal global shape functions under the label 'Coons-patch macroelements' (CPM) have been previously proposed and used in conjunction with the finite element method and the boundary element method. This paper continues the research on the performance of CPM in conjunction with the collocation method. In contrast to the previous CPM that was based on a Galerkin/Ritz formulation, no domain integration is now required, a fact that justifies the name 'integration-free Coons macroelements. Therefore, in addition to avoiding mesh generation, and saving human effort, the proposed technique has the additional advantage of further reducing the computer effort. The theory is supported by five test cases concerning Poisson and Laplace problems within 2D smooth quadrilateral domains. Copyright (C) 2008 John Wiley & Sons, Ltd.