Nonsmooth data error estimates for FEM approximations of the time fractional cable equation

作者：Zhu, Peng^*; Xie, Shenglan; Wang, Xiaoshen

来源：Applied Numerical Mathematics, 2017, 121: 170-184.

DOI：10.1016/j.apnum.2017.07.005

• Fractional cable equation
• Convolution quadrature
• Finite element method
• Riemann-Liouville fractional derivative
• Nonsmooth data error estimate

In this paper, the fractional cable equation, involving two Riemann-Liouville fractional derivatives, with initial/boundary condition is considered. Two fully discrete schemes are obtained by employing piecewise linear Galerkin FEM in space, and using convolution quadrature methods based on the first- and second-order backward difference methods in time. Optimal error estimates in terms of the initial data and the inhomogeneity for the semi-discrete scheme and fully discrete schemes are discussed. Numerical results are shown to verify the theoretical results.

• 出版日期2017-11
• 单位嘉兴学院