We present a p-adaptive discontinuous Galerkin (DG) approach for solving second-order elastic and acoustic wave equations. An arbitrary anisotropic medium is considered, and the first- to fourth-order polynomials are used. The second-order wave equation is first transformed into a unified first-order hyperbolic system that is suitable for the DG method. In the following, we describe the p-adaptive DG algorithm in detail. The adaptation criterion using the area indicator is adopted, and the order of polynomial applied for each subdomain in the whole computational domain is marked before time evolution. The adaptation used for wave propagation simulation is practical and flexible, and various numerical fluxes can be directly incorporated into this p-adaptive DG algorithm. Two numerical examples are used to demonstrate the performance of the proposed adaptive scheme.

中文翻译：

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求解二阶地震波方程的p自适应间断伽辽金法


我们提出了一种用于求解二阶弹性波方程和声波方程的 p 自适应间断伽辽金 (DG) 方法。考虑任意各向异性介质，并使用一阶至四阶多项式。首先将二阶波动方程转化为适合DG方法的统一一阶双曲系统。下面，我们详细描述p自适应DG算法。采用面积指标的自适应准则，在时间演化之前标记整个计算域中每个子域所应用的多项式的阶数。用于波传播模拟的自适应方法实用且灵活，各种数值通量可以直接纳入该 p 自适应 DG 算法中。使用两个数值示例来证明所提出的自适应方案的性能。