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Αθήνα,  24/11/2015

Δ Ι Α Λ Ε Ξ Η

Ομιλητής: Δουγαλής Βασίλειος
               Παν. Αθηνών και Ι.Τ.Ε.
                   
                         
Τίτλος : « Finite element method for the Shallow Water equations with characteristic boundary conditions »

Περίληψη :  In this talk I will present some joint results with D.C. Antonopoulos, an extended version of which may be found in   arXiv: 1507.08209. In that work we consider the Shallow Water equations (SW) in one space dimension, posed on a finite interval, in the subcritical or supercritical flow regimes. At the endpoints of the interval we impose characteristic boundary conditions, that, as is well known, are transparent for the SW. The initial-boundary value problems (ibvp’s) for the SW under these boundary conditions are known to possess smooth solutions, locally in time. We discretize the ibvp’s in space using the standard Galerkin -finite element method with continuous, piecewise polynomial functions of degree r-1 , r ≥ 2, on a quasiuniform mesh with maximum meshlength h, and prove, in the case of smooth solutions, error estimates in L2  of the resulting semidiscretizations with error bounds of O(hr-1) when r ≥ 3.

We consider in particular the spatial discretization with piecewise linear continuous functions,   which possesses an L2 error bound of O(h2) in the case of uniform mesh, and discretize the resulting semidiscrete problem in time using the classical, explicit, fourth-order accurate Runge-Kutta method. The fully discrete problem can be implemented in a straightforward way for both flow regimes considered, and it is stable under a Courant - number restriction. We test the method in several numerical experiments involving subcritical and supercritical flows, and conclude that the numerical characteristic boundary conditions are highly absorbing.

Η ομιλία θα δοθεί την Παρασκευή 4 Δεκεμβρίου 2015  και ώρα 13:35, στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών, κτ. Ε΄, 2ος όροφος.
                               

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