Numerical solution of the two-dimensional Poincaré equation
| Autor: | Gerard L. G. Sleijpen, Arno Swart, Jan Brandts, Leo R. M. Maas |
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| Přispěvatelé: | Analysis (KDV, FNWI) |
| Rok vydání: | 2007 |
| Předmět: |
Discretization
Numerical analysis Applied Mathematics Mathematical analysis Motion (geometry) Boundary (topology) Base (topology) Ill-posed problems Regularization (mathematics) Poincar´e equation Regularisation symbols.namesake Computational Mathematics Exact solutions in general relativity internal waves Poincaré conjecture symbols regularisation Poincaré equation Internal waves Wiskunde en Informatica Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics, 200(1), 317-341. Elsevier |
| ISSN: | 0377-0427 |
| Popis: | This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers. Inspired by the hyperbolicity of the equation we propose a discretisation particularly suited for this problem, which results in matrices whose size varies linearly with the number of grid points along the coordinate axes. Exact solutions are obtained, defined on a perturbed boundary. Furthermore, the problem is seen to be ill-posed and there is need for a regularisation scheme, which we base on a minimal-energy approach. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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