空间Riesz分数阶方程的时空线性有限元法

A space-time linear finite element method for Riesz space fractional equations

对于时间方向二阶导数的空间Riesz分数阶微分方程,构造了一个时空线性有限元全离散计算格式。时间方向采用时间线性有限元计算,空间方向采用线性有限元离散,获得了计算方法的显式表达式,证明了计算方法的稳定性。进行数值实验验证了方法的有效性。

For the Riesz space fractional order differential equation with second order derivative in the time direction, a space-time linear finite element fully discrete computational scheme is established. In the time direction the time linear finite element is used to compute, in the space direction the linear finite element is applied to discrete, the explicit formulation for this method is obtained, and the stability for this computational method is proved. Some numerical tests are given for verification of this method.