A nonconforming spectral element ocean model

A nonconforming spectral element ocean model, which allows a combination of higher- and lower-order elements in a single formulation, is presented. The choice between the order of interpolating polynomials and the number of elements can be adjusted locally in a subregion of a domain, based on the geometric and dynamic properties of a solution. High-order elements are applied in regions with smooth properties and achieve high-order convergence rates. In the regions where smoothness of the solution is limited and/or geometric requirements are complex, low-order elements are used. This paper presents a nonconforming spectral element method based on mortar elements. Convergence of the method is analyzed using several elliptic and hyperbolic test problems in two and three dimensions. To test the method, a study of wave propagation through a nonconforming interface for two problems in a realistic geometry is also presented.

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