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.

中文翻译：

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全球潮汐模型的混合有限元

我们研究了具有线性阻力和强迫项的线性化旋转浅水方程的混合有限元方法。通过对线性动量的等效二阶公式进行强能量估计，我们证明了系统在没有能量积累的情况下的长期稳定性 - geotryptic 状态。线性化动量和自由表面高程的先验误差估计以 $$L^2$$L2 以及线性化动量的时间导数和散度给出。数值结果证实了关于能量阻尼和收敛速度的理论结果。