Analysis of discrete finite element shallow-water models

Authors: Rostand, Virgile
Advisor: Le Roux, Daniel
Abstract: The shallow-water equations system plays a central role in numerical oceanic models. The finite element method is particularly well suited to solve the shallow-water equations as it works on irregular meshes with a variety of approximation spaces. However, the behavior of the numerical solution highly depends on the interaction between these approximation spaces. For specific finite element pairs the solution may exhibit spurious oscillations induced by the discretization scheme. In this thesis, we analyze these oscillations for a wide selection of finite element pairs. The numerical dispersion of inertia-gravity waves is quantified with dispersion analyses. A constructive linear algebra approach is developed to compute the kernels of the discretized operators. The results are used to characterize the smallest representable vortices on both structured and unstructured meshes. A special attention is given to the Raviart-Thomas and Brezzi-Douglas-Marini approximation spaces.
Document Type: Thèse de doctorat
Issue Date: 2007
Open Access Date: 13 April 2018
Grantor: Université Laval
Collection:Thèses et mémoires

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