Moving finite element methods for time fractional partial differential equations

With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuniform meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations (FPDEs). The unconditional stability and convergence rates of 2 - α for time and r for space are proved when the method is used for the linear time FPDEs with α -th order time derivatives. Numerical examples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.