抛物型方程在变动区域中的Galarkin有限元法及其对Stefan问题的应用

Finite Elemente Method for the Parabolic Equation in a Variable Domain With Its Application to the Stefan Problem

文中叙述了具变系数抛物型方程在变动区域中的有限元半离散格式和全离散θ格式,给出了误差界和稳定性结果,并应用于求解Stefan问题。

A discretization of finite element method for the parabolic equation with variable coefficient in a time-dependent domain is considered. Scheme of semidiscretization and θ-scheme are given. Error estimation and theorem of stability are considered. Application to Stefan problem is given,with an iterative algorithm to follow the moving boundary. Numerical results agree well with the theoretical error bounds.