Fast Implementation of Explicit Time Stepping Algorithms with the Finite Element Method for a Class of Nonlinear Evolution Problems

摘要

It is shown that, under special conditions, the application of the product approximation variation of the Galerkin method for nonlinear evolution problems in the finite element method results in constant (i.e., time independent) matrices. Computing required to solve these equations with an explicit time-stepping algorithm is decreased considerably compared to the standard Galerkin formulation in which the matrices are time dependent. The method is applied to the shallow water equations and a nonlinear heat conduction problem.