SUMMARYWe build and analyze a Runge-Kutta Discontinuous Galerkin method to approximate the one-and two-dimensional Shallow-Water Equations. We introduce a flux modification technique to derive a wellbalanced scheme preserving steady-states at rest with variable bathymetry and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.

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We consider finite volume methods for the Stokes system in a polyhedral domain of R d , d = 2 or 3. We prove different error estimates using non-conforming tools, namely by regarding the finite volume scheme as a non-conforming approximation of the continous variational problem. This point of view allows us to extend recent error estimates obtained by Blanc et al. (2004, Numer. Meth. PDE, 20, 907-918.) for equilateral triangulations to a larger class of 2D meshes (incompletely proved by Alami-Idrissi & Atounti (2002) JIPAM, 3, for meshes made of triangles) and to obtain its 3D version. Some numerical tests confirm our theoretical considerations.

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