Mixed finite elements for global tide models
For computational geophysics, this provides theoretical guarantees for global tide models using mixed finite elements.
The paper proves long-time stability and derives a priori error estimates for mixed finite element methods applied to linearized rotating shallow water equations, with numerical results confirming energy damping and convergence rates.
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.