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 L2 error estimate for the linear case with the convergence rate through analysis.
Ren, Z., Wei, L., He, Y., & Wang, S. (2012). Numerical analysis of an implicit fully discrete local discontinuous Galerkin method for the fractional Zakharov–Kuznetsov equation. Mathematical Modelling and Analysis, 17(4), 558-570. https://doi.org/10.3846/13926292.2012.708675
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through analysis.