发展型方程的时间间断时空有限元方法

The Time Discontinuous Finite Element Method for Evolution Equations

时空有限元方法通过统一时间和空间变量,克服了传统有限元方法对时间作差分离散引起的时间上的低精度,不但具有时、空高精度,而且在无结构网格上耗散特性好、无条件稳定,成为解决时间依赖问题的有效方法.本文利用抛物问题给出时间允许间断而空间连续的时空有限元方法的基本概念和过程,给出抛物型方程、积分-微分方程、双曲方程、Sobolev方程和其他高阶方程的算例,验证方法的精度和稳定性,并综合评价时间间断时空有限元方法目前的发展现状和应用前景.

Unifying the space and time variables, space-time finite element method over- comes the low order accuracy in traditional finite element method caused by the difference discrete in time. This method has high-order accuracy in space and time directions, good dis- sipation on unstructured mesh, unconditional stablity. Thus it becomes an efficiency method for the problems dependent on time. In this paper, the basic conceptions and formulations of the space-time finite element method, discontinuous in time and continuous in space, are given by a general parabolic model problem. The numerical simulation results for parabolic equations, integral-differential equations, hyperbolic problems, Sobolev equations and other high order equations are given to illustrate the stability and accuracy. The development and applied foreground are discussed for the time discontinuous space-time finite element method.