A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling
A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling
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DOI：
10.1016/j.ocemod.2008.09.002
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发表时间：
2008-05
期刊：
影响因子：
3.2
通讯作者：
Colin J. Cotter;David A. Ham;Christopher C. Pain
中科院分区：
文献类型：
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作者：
Colin J. Cotter;David A. Ham;Christopher C. Pain
我们引入了用于海洋建模的混合不连续/连续有限元对，具有连续二次层厚度和不连续速度。我们研究了应用于 f 平面上的线性浅水方程的有限元对。该元素对具有以下性质：强烈满足边界条件的所有地转平衡状态的离散散度恰好等于零，因此恰好是离散方程的稳态。这意味着有限元对具有优异的地转平衡特性。我们还表明，应用于非旋转线性浅水方程的元素对不具有任何虚假的小特征值。我们使用数值测试来说明这些属性，并提供收敛计算，表明数值解的误差随着速度和层厚度的单元边缘长度呈二次方衰减。
We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f-plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete divergence equal to exactly zero and hence are exactly steady states of the discretised equations. This means that the finite element pair has excellent geostrophic balance properties. We also show that the element pair applied to the non-rotating linear shallow-water equations does not have any spurious small eigenvalues. We illustrate these properties using numerical tests and provide convergence calculations which show that the numerical solutions have errors which decay quadratically with element edge length for both velocity and layer thickness.