A Space-Time Finite Element Method for the Fractional Ginzburg–Landau Equation

Abstract

A fully discrete space-time finite element method for the fractional Ginzburg–Landau equation is developed, in which the discontinuous Galerkin finite element scheme is adopted in the temporal direction and the Galerkin finite element scheme is used in the spatial orientation. By taking advantage of the valuable properties of Radau numerical integration and Lagrange interpolation polynomials at the Radau points of each time subinterval In, the well-posedness of the discrete solution is proven. Moreover, the optimal order error estimate in L∞(L2) is also considered in detail. Some numerical examples are provided to evaluate the validity and effectiveness of the theoretical analysis.

Keywords

• fractional Ginzburg–Landau equation
• discontinuous Galerkin finite element method
• error estimate
• numerical test