瞬变温度场问题的有限元解法和最大模原理

在二维区域Ω(边界为?Ω)上,描述变温过程的抛物型方程及其初边值条件为式中,T为温度,α为导温系数,Q(x,y,t)为相应于热源的已知函数,T_0(x,y)为初始温度,g(x,y,t)为已知的边界温度. 用有限元法求解瞬变温度场问题,通常从变分原理出发,假设温度对时间的导数与温度一样为分片线性函数.它导出的热容量矩阵是非对角型的,我们称之为算法I.采用

THE FINITE ELEMENT METHOD OF THE TRANSIENT HEAT CONDUCTION EQUATION AND THE PRINCIPLE OF MAXIMUM NORM

This paper sets up the prineiple of maximum norm for the finite element methodin 1] to solve the problem of the transient heat conduction equation and explains thecauses of strange temperature values in the initial stage of computation. Based onthe conservation principle of heat flow, we present another finite element method tosolve this problem and show the principle of maximum norm about that. Comparing with the former, our method will relax the requirements to steps oftime and space and will bring out great convenience for the theoretical analysis andthe practical computation.