Robert Kirby
Baylor University
"Mixed finite elements for nonlinearly damped tide models"
Regional and global tides are modeled by a hyperbolic PDE system, the linearized shallow water equations with Coriolis force and damping due to bottom friction. Many friction models depend nonlinearly on the velocity, which greatly complicates the analysis of these problems. We present mixed finite element discretizations of these equations and describe stability and continuous dependence results for the semidiscrete as well as PDE systems. These results give effective damping rates for various nonlinearities as well as rates at which differing initial conditions approach a global attracting solution, and also lead to a priori error estimates for the finite element solution. In addition to common results that are optimal in h with exponential increase in time, we also present a priori estimates that are uniform in time, although at a suboptimal rate in h.
Host: Kyle Mandli
