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Prof. Francis X. Giraldo

Department of Applied Mathematics, Naval Postgraduate School, Monterey California USA

High-Order Continuous (CG) and Discontinuous Galerkin (DG) Semi-Implicit Methods for the Solution of the Euler and Shallow Water Equations

Abstract:

In this talk, I will describe the numerical methods that we have been developing for solving, primarily, hyperbolic equations. These methods are high-order accurate, local in nature, and have some very nice properties such as local conservation and high parallel efficiency. In order to consider using these methods for large-scale applications such as in an operational-like setting requires the introduction of implicit time-integrators. In this talk, I will describe how semi-implicit time-integrators can be combined with high-order CG and DG methods. To simplify the discussion we shall concentrate on the 2D Euler and shallow water equations. In addition, I will also discuss a new approximation on the triangle that we have developed which, we think, will offer much more efficiency to numerical models based on either CG or DG methods; unfortunately, up to now, we have only been able to construct such approximations for polynomial degrees <= 7.
Datum: 09.02.2007
Zeit:14.15
Ort:FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin.
Raum:032 im Erdgeschoss

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