论文标题
在非现行电网上具有粗糙速度场的离散对流方程
Discretizing advection equations with rough velocity fields on non-cartesian grids
论文作者
论文摘要
我们研究对流方程的离散化的特性一般而言是非现行的网格和图形的。在非现行电网上离散的对流方程仍然是一个长期存在的挑战，因为网格的结构也会导致溶液中的强烈振荡，即使对于其他恒定的速度场也可以导致溶液中的强烈振荡。我们引入了一种新方法，以跟踪任何图上粗糙速度字段的解决方案的振荡。该方法特别突出了网格上的一些固有结构条件，以在解决方案上传播规律性。
We investigate the properties of discretizations of advection equations on non-cartesian grids and graphs in general. Advection equations discretized on non-cartesian grids have remained a long-standing challenge as the structure of the grid can lead to strong oscillations in the solution, even for otherwise constant velocity fields. We introduce a new method to track oscillations of the solution for rough velocity fields on any graph. The method in particular highlights some inherent structural conditions on the mesh for propagating regularity on solutions.
