A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations
作者：
Highlights：
• A well-balanced DG method adopts the one-stage ADER approach for the temporal discretization.
• This method applies the differential transformation procedure to express the spatiotemporal expansion coefficients of the solution through the low order spatial expansion coefficients recursively.
• The proposed method is one-step, one-stage, fully-discrete, and easily proceeds to arbitrary high order accuracy in space and time without much coding effort.
• The method is more efficient than the Runge-Kutta DG method with the same order of accuracy.
摘要
•A well-balanced DG method adopts the one-stage ADER approach for the temporal discretization.•This method applies the differential transformation procedure to express the spatiotemporal expansion coefficients of the solution through the low order spatial expansion coefficients recursively.•The proposed method is one-step, one-stage, fully-discrete, and easily proceeds to arbitrary high order accuracy in space and time without much coding effort.•The method is more efficient than the Runge-Kutta DG method with the same order of accuracy.
论文关键词：Shallow water equations,Discontinuous Galerkin method,ADER Approach,Differential transformation procedure,Well-balancing,Fully-discrete
论文评审过程：Received 12 May 2020, Revised 26 November 2020, Accepted 30 November 2020, Available online 23 December 2020, Version of Record 23 December 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125848
