Name
Title | ||
|---|---|---|
Global superconvergence of simplified hybrid combinations for elliptic equations with singularities, I. Basic theorem |
Abstract | ||
|---|---|---|
To solve the elliptic boundary value problems with singularities, the simplified hybrid combinations of the Ritz-Galerkin and finite element methods (RGM-FEM) are explored to lead to the global superconvergence rates on the entire solution domain, based on an a posteriori interpolation techniques of Lin and Yan [12] that only cost a little more computation. Let the solution domain S=S1?S2?і and S17S2=Ë. Suppose that S1 can be partitioned into quasiuniform rectangles: S1=~ijij, a singular point occurs at ‘S2, and the singular functions are chosen in S2. Then for bilinear elements, it is proven that the simplified hybrid combinations of RGM-FEM can provide the global superconvergence rate O(h2) for solution gradients over the entire subdomains S1 and S2, where h is the maximal boundary length of ij. The global superconvergence O(h2) is better, compared to O(h2mi), 0iԁ given in [4, 9]. Note that numerical stability of the simplified hybrid combinations of RGM-FEM is also optimal [6]. This paper presents the important results for the general case of Poisson-problems on a polygonal domain S estimates for the Sobolev norm ||·||1, given in a much more general sense than known before, cf. [1-4, 14-18]. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1007/s006070050011 | Computing |
Keywords | Field | DocType |
AMS Subject Classifications: 65N10,65N30.,Key Words: Elliptic equation,singularity problem,superconvergence,combined method. | Discretization,Mathematical optimization,Mathematical analysis,A priori and a posteriori,Superconvergence,Decomposition method (constraint satisfaction),Finite element method,Partial differential equation,Elliptic curve,Domain decomposition methods,Mathematics | Journal |
Volume | Issue | ISSN |
65 | 1 | 0010-485X |
Citations | PageRank | References |
1 | 0.63 | 0 |
Authors | ||
1 | ||