Combinat ions of Col locat ion and F in i t e -

Abstract

Abstract--In this paper, we provide a framework of combinations of collocation method (CM) with the finite-element method (FEM). The key idea is to link the Galerkin method to the least squares method which is then approximated by integration approximation, and led to the CM. The new important uniformly Vh0-elliptic inequality is proved. Interestingly, the integration approximation plays a role only in satisfying the uniformly Vh0-elliptic inequality. For the combinations of the finiteelement and collocation methods (FEM-CM), the optimal convergence rates can be achieved. The advantage of the CM is to formulate easily linear algebraic equations, where the associated matrices are positive definite but nonsymmetric. We may also solve the algebraic equations of FEM and the collocation equations directly by the least squares method, thus, to greatly improve numerical stability. Numerical experiments are also carried for Poisson's problem to support the analysis. Note that the analysis in this paper is distinct from the existing literature, and it covers a large class of the CM using various admissible functions, such as the radial basis functions, the Sinc functions, etc. (~) 2006 Elsevier Ltd. All rights reserved.

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Cite this paper

@inproceedings{Hu2006CombinatIO, title={Combinat ions of Col locat ion and F in i t e -}, author={Hsin-Yun Hu and Zi-Cai Li}, year={2006} }