Equidistributing principles in moving finite element methods
This note consideres the moving finite element method based on a least squares principle and one using a Petrov-Galerkin approach. The authors compare this two methods. A common feature of both methods is that they move the nodes according to an approximate equidistributing principle though in the original derivation of the difference equations governing the movement of the nodes no equidistributing principle was used explicitly. The penalty function of K. Miller and his coworkers designed for the least squares method is shown to be convenient for using in the Petrov- Galerkin method too. Finally, numerical examples illustrating the performance of the two methods are given. The Petrov-Galerkin method gives a more accurate solution than the least squares one (with or without product approximation).
scientific article; zbMATH DE number 3844977
scientific article