Journal
COMPUTING
Volume 82, Issue 2-3, Pages 103-119Publisher
SPRINGER WIEN
DOI: 10.1007/s00607-008-0003-x
Keywords
DUNE; hierarchical grids; interface; finite elements; finite volumes; entity complex; geometric realization; father relation; index maps; parallelization
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We give a mathematically rigorous definition of a grid for algorithms solving partial differential equations. Unlike previous approaches (Benger 2005, PhD thesis; Berti 2000, PhD thesis), our grids have a hierarchical structure. This makes them suitable for geometric multigrid algorithms and hierarchical local grid refinement. The description is also general enough to include geometrically non-conforming grids. The definitions in this article serve as the basis for an implementation of an abstract grid interface as C++ classes in the framework (Bastian et al. 2008, this issue).
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