An adaptive multi-grid algorithm for the numerical solution of quasilinear potential equations
type: Item
instance of: scholarly article
title: An adaptive multi-grid algorithm for the numerical solution of quasilinear potential equations
zbMATH Open document ID: 0572.65090
DOI: 10.1007/BF02240197
author: B. George
published in: Computing
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 31A25
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 3913614
zbMATH Keywords: quasilinear potential equations
zbMATH Keywords: adaptive multi-grid algorithm
zbMATH Keywords: error estimation
zbMATH Keywords: numerical experiments
zbMATH Keywords: minimal surface problem
zbMATH Keywords: comparison
MaRDI profile type: Publication
cites work: Solution of Large Sparse Nonlinear Systems by Monotone Convergent Iterations and Applications
cites work: Multi-Level Adaptive Solutions to Boundary-Value Problems
cites work: Numerical Solution of the Minimal Surface Equation
cites work: Q4130879
cites work: Q3909923
cites work: Zur Diskretisierung nichtlinearer elliptischer Differentialgleichungen. (On the discretization of nonlinear elliptic differential equations)
cites work: Q4404374
description: scientific article; zbMATH DE number 3913614