自适应间断有限元方法求解双曲守恒律方程

Adaptive Discontinuous Galerkin Methods for Hyperbolic Conservation Laws

研究自适应Runge-Kutta间断Galerkin(RKDG)方法求解双曲守恒律方程组,并提出两种生成相容三角形网格的自适应算法.第一种算法适用于规则网格,实现简单、计算速度快.第二种算法基于非结构网格,设计一类基于间断界面的自适应网格加密策略,方法灵活高效.两种方法都具有令人满意的计算效果,而且降低了RKDG的计算量.

For systems of nonlinear hyperbolic conservation laws, two adaptive discontinuous Galerkin finite element methods （ADGM） generating conforming unstructured triangular meshes are proposed. The first one is for structured mesh. It is simple and fast. The second one is for both structured and unstructured meshes. Based on posteriori error estimation of nonlinear hyperbolic conservation laws, a discontinuous interfacial mesh refinement indicator is shown in generating adaptive meshes. It is shown that the methods are flexible and reliable. Computation cost is decreased.