论文标题
一种用于网络传输方程的混合不连续的Galerkin方法
A hybrid discontinuous Galerkin method for transport equations on networks
论文作者
论文摘要
我们讨论了一维网络上传输问题的数学建模和数值离散化。得出了合适的耦合条件，以确保跨网络连接的质量保护和数学能量的耗散，从而证明存在独特的解决方案。然后，我们考虑通过混合不连续的盖尔金方法进行空间离散化，该方法提供了合适的上风机制来处理运输问题，并允许自然方式合并耦合条件。另外，该方法继承了质量保护和连续问题的稳定性。订单最佳收敛速率由数值测试建立并说明。
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a mathematical energy which allows to prove existence of unique solutions. We then consider the space discretization by a hybrid discontinuous Galerkin method which provides a suitable upwind mechanism to handle the transport problem and allows to incorporate the coupling conditions in a natural manner. In addition, the method inherits mass conservation and stability of the continuous problem. Order optimal convergence rates are established and illustrated by numerical tests.
