Kirby, Robert C.2019-12-042019-12-042019-082019-07-24August 201https://hdl.handle.net/2104/10780We describe finite element methods for the linearized rotating shallow water equations which govern tides. Symplectic Euler and Crank-Nicolson time-stepping strategies have good energy preservation properties, which is desirable for tide modeling, but require careful treatment of linear algebra. For symplectic Euler, we have to invert the Raviart-Thomas element mass matrix at every time step. Thus we give estimates for the eigenvalues of these mass matrices. Crank-Nicolson, being fully implicit, has a more complicated system of equations which requires inverting the entire system. For this, we present an effective block preconditioner using parameter-weighted norms in H(div). We give results that are nearly dependent of the given constants. Finally, we provide numerical results that confirm this theory.application/pdfenFinite elements. Mixed methods. Preconditioning. Tide model. Rotating shallow water equations.ThesisWorldwide access2019-12-04