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**Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle.**
*(English)*
Zbl 0806.65092

The authors derive several moving mesh partial differential equations based on the equidistribution principle (MMPDE). Among them are moving mesh methods that are constructed by time differentiation of quasi-state equidistribution principles (QSEP), and that are based on attraction and repulsion pseudoforces between the nodes of the grid and on strategies involving a correction term. In most of them a term appears that serves as a source of mesh movement and can also be regarded as a mechanism to pull the mesh back toward equidistribution of a monitor function when it drifts away from equidistribution. So in this sense such MMPDEs can be considered to be closely related to the QSEP. A stability analysis of the proposed methods is presented. It is pointed out that a key term for most of these schemes is a term that measures the level of equidistribution. The effectiveness of the suggested methods is demonstrated on interesting numerical experiments.

Reviewer: P.Matus (Minsk)

### MSC:

65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |