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中文摘要：
工程实际中的许多间断问题，例如空气动力学中的激波问题，其数学模型大都是非线性双曲守恒律方程．本文在Runge—Kutta间断Galerkin（RKDG）框架下，结合h型白适应方法处理了一维非线性守恒律方程初值问题和初边值问题．此方法不仅能准确描述间断的出现和位置，而且还能在间断附近适当加密网格，提高计算效率．最后，数值算例验证了算法的有效性．
英文摘要：
Some discontinuous problems like the shock wave problem of aerodynamics can be described by a nonlinear hyperbolic conservation law. In this paper, we present a adap- tive discontinuous Galerkin method for the initial value and initial-boundary value problem of one-dimensional nonlinear hyperbolic conservation law. The method introduces a h-adaptive strategy in the framework of Runge-Kutta discontinuous Galerkin finite element （RKDG）. Then the appearance and position of discontinuity is captured by the method, and the mesh is prop- erly refined near the discontinuity to improve calculation efficiency. Finally, the correctness of the propose results is verified by numerical examples.
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