A tent pitching scheme motivated by Friedrichs theory
Provides a new numerical method for advective Friedrichs systems, but the impact is limited to a specific class of PDEs and the results are only for a 1D model problem.
The paper develops an explicit space-time finite element scheme for Friedrichs systems, leveraging a weak continuity property at inflow-outflow boundary intersections. Numerical results for a 1D wave propagation problem are shown.
Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the continuity property, is designed. Numerical results for a model one-dimensional wave propagation problem are presented.