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arXiv · 2003.01632

Preconditioning mixed finite elements for tide models

Tate Kernell·Robert C. Kirby
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Abstract

We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject to a CFL-like stability condition, it requires the inversion of a linear system at each step. We develop weighted-norm preconditioners for this algebraic system that are nearly robust with respect to the physical and discretization parameters in the system. Numerical experiments using Firedrake support the theoretical results.

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Tate Kernell, Robert C. Kirby. 2020-03-03. Preconditioning mixed finite elements for tide models. https://arxiv.org/abs/2003.01632

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