An algorithm for adaptive mesh refinement inn dimensions |
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Authors: | C T Traxler |
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Affiliation: | 1. Institut für Theoretische Physik, Universit?t Gie?en, Heinrich-Buff-Ring 16, D-35392, Gie?en, Federal Republic of Germany
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Abstract: | The author describes a fast algorithm for local adaptive mesh refinement inn dimensions based on simplex bisection. A ready-to-use implementation of the algorithm in C++ pseudocode is given. It is proven
that the scheme satisfies all conditions one usually places on grid refinement in the context of finite-element calculations.
Bisection refinement also offers an interesting additional feature over the usual, regular, refinement scheme: all linear
finite-element basis functions of one generation are of disjoint support. In the way the scheme is presented here, all generated
simplex meshes satisfy a ‘structural condition’ which is exploited to simplify bookkeeping of the neighbour graph. However,
bisection refinement places certain restrictions on the initial, coarsest grid. For a simply connected domain, a precise and
useful criterion for the applicability of the described refinement scheme is formulated and proven. |
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Keywords: | 65N50 |
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