Affiliation:
1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
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.
Funder
Natural Science Foundation of Inner Mongolia
Program for Innovative Research Team in Universities of the Inner Mongolia Autonomous Region
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Reference47 articles.
1. Theory and Applications of Fractional Differential Equations; Elsevier Science: London, UK, 2006;Kilbas;J. Comput. Phys.,2017
2. Podlubny, I. (1999). Fractional Differential Equations, Academic Press.
3. Some applications of fractional equations;Weitzner;Commun. Nonlinear Sci. Numer. Simul.,2003
4. Fractional Ginzburg-Landau equation for fractal media;Tarasov;Phys. A,2005
5. Fractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media;Milovanov;Phys. Lett. A,2005
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献