A discontinuous Galerkin finite element method for the Zakharov-Kuznetsov equation

作者：Sun, Huixia; Liu, Lijie; Wei, Leilei^*

来源：Advances in Difference Equations, 2016, 2016(1): 158.

DOI：10.1186/s13662-016-0890-7

• Zakharov-Kuznetsov equation
• discontinuous Galerkin method
• stability
• error estimate

In this paper, we develop and analyze a discontinuous Galerkin (DG) method for the two-dimensional nonlinear Zakharov-Kuznetsov (ZK) equation. The DG method could be applied without introducing any auxiliary variables or rewriting the original equation into a larger system. Stability and an error estimate are discussed carefully. Finally, a numerical example for the nonlinear problem is given to show that the scheme attains the optimal (k + 1)th order of accuracy for piecewise Q(k) polynomials of degree k when k >= 2.

• 出版日期2016-6-18
• 单位河南工业大学