Name
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 V^0"h-elliptic inequality is proved. Interestingly, the integration approximation plays a role only in satisfying the uniformly V^0"h-elliptic inequality. For the combinations of the finite-element 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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.camwa.2005.10.018 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
integration approximation,collocation method,galerkin method,finite-element method,algebraic equation,least squares method,poisson's equation,collocation equation,squares method,combined method,numerical experiment,linear algebraic equation,h-elliptic inequality,radial basis function,finite element,linear algebra,positive definite,least square method,numerical stability,satisfiability,finite element method,poisson s equation | Least squares,Mathematical optimization,Orthogonal collocation,Mathematical analysis,Galerkin method,Algebraic equation,Finite element method,Collocation method,Numerical stability,Mathematics,Collocation | Journal |
Volume | Issue | ISSN |
51 | 12 | Computers and Mathematics with Applications |
Citations | PageRank | References |
1 | 0.40 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hsin-Yun Hu | 1 | 2 | 1.43 |
| Zi-Cai Li | 2 | 125 | 18.79 |