Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
The authors present a useful review of 116 papers devoted to grid methods with adaptive distributions of nodes. Finite-element and difference methods with such adaptations are very efficient for nonstationary problems that contain moving regions of rapid change in functions to be found. In particular, problems of hydrodynamics and gas dynamics should be mentioned. Adaptive techniques include minimization or equidistribution of the error measure integral. Methods based on attraction and repulsion pseudoforces between nodes are considered as well. In my opinion, a few important results in the field under consideration have been published by Russian authors like S. K. Godunov and others.
scientific article; zbMATH DE number 4213355
scientific article