Abstract. We propose a mixed discontinuous Galerkin method for the bending problem of Naghdi shell, and present an analysis for its accuracy. The error estimate shows that when components of the curvature tensor and Christoffel symbols are piecewise linear functions, the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the...

In this paper a locking-free method, using mixed nite elements, is introduced to approximate the soluton of Naghdi shell problems with small parameter t, the thickness of the shell. The approach of Arnold and Brezzi 1] is employed with some important changes. Instead of proving the discrete Inf-Sup condition for arbitrary geometric coeecients, which does not seem possible, we prove a weaker sta...

Abstract Diffraction and refraction of nonlinear shallow water waves due to uneven bathymetry are studied by use the Green–Naghdi (GN) equations in three dimensions. A numerical wave tank consisting deep, transitional, regions is created. Various forms three-dimensional bathymetry, ramps with nonuniform profiles large slopes, used connect deep-water side shelf. wavemaker placed at upwave domain...