In this paper, we introduce and analyze discontinuous Galerkin methods for a Naghdi type arch model. We prove that, when the numerical traces are properly chosen, the methods display optimal convergence uniformly with respect to the thickness of the arch. These methods are thus free from membrane and shear locking. We also prove that, when polynomials of degree k are used, all the numerical tra...

A nonlinearly elastic shell is modeled either by the nonlinear threedimensional shell model or by a nonlinear two-dimensional shell model. We show how such two-dimensional shell models can be derived from the minimization problem associated with the nonlinear three-dimensional shell model. For shells made of a Saint Venant-Kirchhoff material, we obtain in particular the nonlinear shell models o...

We introduce a new class of two-dimensional fully nonlinear and weakly dispersive Green-Naghdi equations over varying topography. These new Green-Naghdi systems share the same order of precision as the standard one but have a mathematical structure which makes them much more suitable for the numerical resolution, in particular in the demanding case of two dimensional surfaces. For these new mod...

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic...

The two-dimensional Green–Naghdi equations are studied for the case of uneven bottom topography. topography function can depend on time. Group classification these with respect to describing is performed using an algebraic approach.

We give some equivalence estimates on the solution of a singular perturbation problem that represents, among other models, the Koiter and Naghdi shell models. Two of the estimates apply to intermediate shell problems and the third is for membrane/shear dominated shells. From these equivalences, many known and some new sharp estimates on the solutions of the singular perturbation problems easily...

We consider the Nagdhi equations which model a thin three-dimensional shell. We propose a spectral discretization of this problem in the case where the midsurface of the shell is weakly regular. We perform the numerical analysis of the discrete problem and prove optimal error estimates. Résumé: Nous considérons les équations de Nagdhi qui modélisent une coque tridimensionnelle de faible épaisse...