Finite-element schemes for extended integrations of atmospheric models

Of the two finite-element models presently used to investigate the effect of the conservation of integral invariants, by means of finite-element discretization schemes of the shallow-water equations, in order to serve as a paradigm of long-term atmospheric-model integrations, the first employs rectangular elements and conserves total energy, while the second uses triangular elements and a high-accuracy two-stage Numerov-Galerkin method. Attention is given to critical times for numerical nonlinear instability, as well as to the determination of the critical degree of dissipation entailed by the achievement of stable long-term integrations. Relative computational efficiency and accuracy comparisons are presented for the two finite-element schemes.