论文标题
当系数矩阵有跳跃时，不连续的盖金光谱元件方案用于波传播
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
论文作者
论文摘要
我们使用具有不连续系数矩阵的线性双曲方程解的$ L_ {2} $规范作为推断不连续的Galerkin Spectral元素方法（DGSEM）的稳定性的替代物。尽管$ l_ {2} $ norm并未受到此类系统的均质和耗散边界条件的初始数据的限制，但$ l_ {2} $ norm范围比由于不连续性而折现增长的规范更容易使用。我们表明，满足Rankine-Hugoniot（或保护）条件的前风数值通量的DGSEM具有与部分微分方程在$ L_ {2} $ Norm中具有相同的能量绑定的能量，再加上额外的耗散，取决于近似解决方案无法满足Rankine-Huginoiot跳跃的程度。
We use the behavior of the $L_{2}$ norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the $L_{2}$ norm is not bounded by the initial data for homogeneous and dissipative boundary conditions for such systems, the $L_{2}$ norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine-Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the $L_{2}$ norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump.
