A variable node finite element method
A new finite element method with variable nodes for integrating partial differential equations in one space dimension is presented. The method utilizes the approximation power of piecewise polynomial functions better than a fixed-node finite element method because it distributes grid points in a nonuniform way to suit the peculiarities of the solution at each instant of time. The method uses the gradient and curvature of the approximating piecewise polynomial itself to determine the position of the nodes rather than physical properties which vary from problem to problem. The method has been implemented in a program VFE which has the exceptional feature of a variable space step as well as a variable time step. Since the method concentrates nodes in regions where small inter- nodal spacing is needed, it is very efficient in integrating equations with shock-like solutions. Finally, the method can be extended to systems of partial differential equations in one dimension and to equations in two dimensions.
scientific article; zbMATH DE number 3880044
scientific article