此篇論文中主要討論使用RKDG有限元素法去計算波動方程和雙曲線型守恆定律的方程式。數值方面，在空間上運用三次多項式和時間上運用TVD Runge-Kutta去迭代，並運用高斯積分的技巧去取代積分和定義投影函數在其中。 最後模擬一些測試問題並得到一些數值結果。

This thesis discusses about using the RKDG finite element methods to compute wave equations and hyperbolic conservation law. From numerical aspect, apply cubic polynomials in space and TVD Runge-Kutta in time to discretize. Then use the technique of Gaussian integration to replace the ordinary integration and define projection in it. Finally, this thesis simulates some test problems and gets some numerical results.

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