在這份論文中，我們使用高階不連續有限元素法解決波方程的模型問題。我們用DG方法對空間作離散，且以 mth-order, m-stage SSP-RK 方法對時間項做迭代。網格部分，我們使用的是四邊型的元素，且多項式基底空間使用 Q^k-polynomials 。數值結果證實了如預期的收斂性，當基底函數設定為 p 階，其數值解的收斂速度為 p+1。

In this work, we develop a high-order Runge-Kutta Discontinuous Galerkin (RKDG) method to solve the two-dimensional wave equations.
We use DG methods to discretize the equations with high order elements in space, and then we use the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme to solve the resulting semi-discrete equations. To discretize the equaiotns in spaces, we use the quadrilateral elements and the Q^k-polynomials as basis functions. The scheme achieves full high-order convergence in time and space while keeping the time-step proportional to the spatial mesh-size.
Numerical results are presented that confirm the expected convergence properties. When all the local spaces contain the polynomials of degree p,the numerical experiments show that the numerical solution converges with order p+1.

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