The fluid dynamic approach to equidistribution methods for grid adaptation

Abstract The equidistribution methods based on L p Monge–Kantorovich optimization and on the deformation method are analyzed primarily in the context of grid adaptation. The first class of methods can be obtained from a variational principle leading to a fluid dynamic formulation based on time-dependent equations for the mass density and the momentum density. In this context, deformation methods arise from a similar fluid formulation by making a specific assumption on the time evolution of the density (but with some degree of freedom for the momentum density). In general, deformation methods do not arise from a variational principle. However, it is possible to prescribe an optimal deformation method, related to L 1 Monge–Kantorovich optimization, by making a further assumption on the momentum density. Thus, the fluid dynamic formulation provides a unified description of equidistribution methods. Some numerical examples using the L p fluid dynamic formulation are also explored.

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