DISCRETIZING ADVECTION EQUATIONS WITH ROUGH VELOCITY FIELDS ON NON-CARTESIAN GRIDS

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)229-303
Number of pages75
JournalQuarterly of Applied Mathematics
Volume82
Issue number2
DOIs
StatePublished - 2024

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this