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 $$L^2$$L2 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.
['Colin J. Cotter', 'Robert C. Kirby']
Mixed finite elements for global tide models