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 Sepúlveda, Paulina, "A Tent Pitching Scheme Motivated by Friedrichs theory" (2015). Mathematics and Statistics Faculty Publications and Presentations. 108.