Discretizing advection equations with rough velocity fields on non-cartesian grids
Analysis of PDEs
2022-11-14 v1 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2211.06311,
title = {Discretizing advection equations with rough velocity fields on non-cartesian grids},
author = {Pierre-Emmanuel Jabin and Datong Zhou},
journal= {arXiv preprint arXiv:2211.06311},
year = {2022}
}