An adaptive multi-grid algorithm for the numerical solution of quasilinear potential equations
This paper describes an iterative method for the numerical solution of a class of quasilinear potential equations using an adaptive multi-grid algorithm (MG-algorithm). The method of solution has been illustrated using one iteration step of MG-cycle. The prolongation and restriction operators, which need coarse-to-fine as well as fine-to-coarse grid transfer, have been chosen of very simple linear structure. A simple error estimation has been carried out to show that the correction equation suggested by \textit{A. Brandt} [Math. Comput. 31, 333-390 (1977; Zbl 0373.65054)] has to be modified to get an efficient MG-algorithm. Another simple approach has been suggested which is based on a two-level version and uses a linear correction equation only on the coarser grid. We also present computational results of several numerical experiments applied on a specific example of the minimal surface problem. A comparison between our methods and other methods applied on the example of the minimal surface problem has been presented.
scientific article; zbMATH DE number 3913614