瞬态热传导方程的时空有限元法

Space-time Finite Element Method for Transient Heat Conduction Equation

基于Gurtin变分原理 ,推导了适用于热传导方程时空有限元法的泛函 ,并对空间域和时间域同时进行离散 ,建立了求解瞬态热传导方程的时空有限元模型 .最后对二维热传导方程采用面向对象技术进行了编程计算 .计算结果表明时空有限元法精度高而且稳定收敛 ,是一种有效的方法 .

The functional of heat conduction equation fitting for space time finite element method is derived. The solid is discreted both in space domain and time domain and the finite element method module for transient heat conduction equation is established. Finally, a two dimension example is programmed and computed. The result shows that the space time finite element method is an efficient method, which provides a more rapid convergence to the exact solutions.