This work was partially supported by the National Science Foundation grants DMS-1318916 and DMS-1216620 and the Air Force Office of Scientific Research grant FA9550-12-1-0484.
Hyperbolic functions, Wave equations, Boundary conditions, Asymptotic properties
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.
Gopalakrishnan, Jay; Monk, Peter; and Sepulveda, Paulina, "A Tent Pitching Scheme Motivated by Friedrichs theory" (2015). Mathematics and Statistics Faculty Publications and Presentations. 108.
This is the author's manuscript of an article subsequently accepted for publication by Elsevier. The version of record can be found on the publisher site.