Continuous finite element methods which preserve energy properties for nonlinear problems

摘要

Continuous finite elements are used to develop numerical methods which preserve energy properties for nonlinear ordinary and partial differential equations. Schemes are constructed that give high orders of accuracy. Time discretization algorithms for the Cahn-Hilliard, Klein-Gordon, Korteweg-de Vries, and Schrödinger equations are presented. Comparisons are made with existing schemes.