## Overlapping Schwarz Methods On Unstructured Meshes Using Non-Matching Coarse Grids (1996)

Venue: | Numer. Math |

Citations: | 49 - 17 self |

### BibTeX

@ARTICLE{Chan96overlappingschwarz,

author = {Tony F. Chan and BARRY SMITH and JUN ZOU},

title = {Overlapping Schwarz Methods On Unstructured Meshes Using Non-Matching Coarse Grids},

journal = {Numer. Math},

year = {1996},

volume = {73},

pages = {149--167}

}

### Years of Citing Articles

### OpenURL

### Abstract

. We consider two level overlapping Schwarz domain decomposition methods for solving the finite element problems that arise from discretizations of elliptic problems on general unstructured meshes in two and three dimensions. Standard finite element interpolation from the coarse to the fine grid may be used. Our theory requires no assumption on the substructures which constitute the whole domain, so each substructure can be of arbitrary shape and of different size. The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved and both the coarse meshes and the fine meshes need not be quasi-uniform. In addition, the domains defined by the fine and coarse grid need not be identical. The one important constraint is that the closure of the coarse grid must cover any portion of the fine grid boundary for which Neumann boundary conditions are given. In this general setting, our algorithms have the same optimal convergence rate of the usual ...

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