Numerical analysis of an implicit fully discrete local discontinuous Galerkin method for the fractional Zakharov–Kuznetsov equation

    Zongxiu Ren Info
    Leilei Wei Info
    Yinnian He Info
    Shaoli Wang Info

Abstract

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  through analysis.

Keywords:

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

How to Cite

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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September 1, 2012
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2012-09-01

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How to Cite

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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