SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1497-A1526, January 2021.
We develop interior penalty discontinuous Galerkin difference methods for the wave equation in second-order form. The new schemes are energy conserving or energy dissipating depending on the simple choice of centered or upwind fluxes and are superconvergent away from boundaries. Unlike analogous methods using standard piecewise polynomial bases, we find that no mesh-dependent penalty parameters are needed to guarantee stability and time step stability constraints for explicit time-marching have a mild dependence on method order. Basic properties of the proposed discretizations are illustrated with numerical experiments in one and two space dimensions.

中文翻译：

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二阶形式波动方程的不连续Galerkin Galerkin差

SIAM科学计算杂志，第43卷，第2期，第A1497-A1526页，2021年1月。
我们为二阶波动方程开发了内部罚分不连续Galerkin差分方法。新的方案是节能或消散能量，这取决于对中心或上风通量的简单选择，并且在边界之外超收敛。与使用标准分段多项式基的类似方法不同，我们发现不需要网格相关的罚分参数来保证稳定性，并且显式时间行进的时间步长稳定性约束对方法顺序的依赖性很小。在一维和二维空间中的数值实验说明了所提出离散化的基本性质。