Name
Abstract | ||
|---|---|---|
In this paper, we consider the problem of solution uniqueness for the second order elliptic boundary value problem, by looking at its finite element or finite difference approximations. We derive several equivalent conditions, which are simpler and easier than the boundedness of the entries of the inverse matrix given in Yamamoto et al., [T. Yamamoto, S. Oishi, Q. Fang, Discretization principles for linear two-point boundary value problems, II, Numer. Funct. Anal. Optim. 29 (2008) 213-224]. The numerical experiments are provided to support the analysis made. Strictly speaking, the uniqueness of solution is equivalent to the existence of nonzero eigenvalues in the corresponding eigenvalue problem, and this condition should be checked by solving the corresponding eigenvalue problems. An application of the equivalent conditions is that we may discover the uniqueness simultaneously, while seeking the approximate solutions of elliptic boundary equations. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.cam.2009.07.040 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
solution uniqueness,equivalent condition,finite element,approximate solution,order elliptic boundary value,elliptic boundary equation,elliptic boundary value problem,t. yamamoto,corresponding eigenvalue problem,finite difference approximation,linear two-point boundary value,finite element method,eigenvalues,finite difference method,finite difference | Boundary value problem,Uniqueness,Finite difference,Mathematical analysis,Finite element method,Finite difference method,Partial differential equation,Elliptic curve,Mathematics,Elliptic boundary value problem | Journal |
Volume | Issue | ISSN |
233 | 2 | 0377-0427 |
Citations | PageRank | References |
1 | 0.41 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zi-Cai Li | 1 | 125 | 18.79 |
| Qing Fang | 2 | 2 | 2.19 |
| Hung-Tsai Huang | 3 | 18 | 4.99 |
| Yi-min Wei | 4 | 1001 | 153.95 |