Interpolated Coefficient Mixed Finite Elements for Semilinear Time Fractional Diffusion Equations

Abstract

In this paper, we consider a fully discrete interpolated coefficient mixed finite element method for semilinear time fractional reaction–diffusion equations. The classic L1 scheme based on graded meshes and new mixed finite element based on triangulation is used for the temporal and spatial discretization, respectively. The interpolation coefficient technique is used to deal with the semilinear term, and the discrete nonlinear system is solved by a Newton-like iterative method. Stability and convergence results for both the original variable and its flux are derived. Numerical experiments confirm our theoretical analysis.

Keywords

• interpolated coefficient mixed finite element method
• semilinear time fractional reaction–diffusion equations
• stability analysis
• convergence analysis