Numerical Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Fractional Zakharoy-Kuznetsoy Equation

作者：Ren, Zongxiu^*; Wei, Leilei; He, Yinnian; Wang, Shaoli

来源：Mathematical Modelling and Analysis, 2012, 17(4): 558-570.

DOI：10.3846/13926292.2012.708675

• time-fractional partial differential equations
• Zakharov-Kuznetsov equation
• local discontinuous Galerkin method
• stability
• error estimates

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov-Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L-2 error estimate for the linear case with the convergence rate O(h(k+1) + (Delta t)(2) + (Delta t)(alpha/2) h(k+1/2)) through analysis.

• 出版日期2012
• 单位河南师范大学; 西安交通大学