We consider two finite element discretizations of the Naghdi equations which model a thin three-dimensional shell. Both of them are derived from a mixed formulation of these equations, and a penalty term is added in the second one. The a posteriori analysis of the discrete problems leads to the construction of error indicators which satisfy optimal estimates. We describe a mesh adaptivity strat...

The main objective of this work is to study the homogeneous thermoelastic interactions in an isotropic hollow thin cylinder immersed electric–magnetic field using linear Moore–Gibson–Thompson theory thermoelasticity, taking into account generalized Ohm’s law. MGT system equations for new model created by incorporating a relaxation period Green–Naghdi type III framework. In addition, Maxwell tha...

A study is made of the propagation of time-harmonic magneto-thermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of Kelvin-Voigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The generalized thermoelasticity theory of type II (Green and Naghdi model) is used to study the propagat...

We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in context of nonlinear dynamics surface water waves under wind forcing, finite depth. The anti-dissipation occurs du to continuos transfer energy wave. find solitary wave solution system, with an increasing amplitude action. This leads blow-up time for infinitely large asymptotic space. dispersive, anti-dissipative and fully phe...

In this paper, we consider discontinuous Galerkin approximations to the solution of Naghdi arches and show how to post-process them in an element-by-element fashion to obtain a far better approximation. Indeed, we prove that, if polynomials of degree k are used, the postprocessed approximation converges with order 2k+1 in the L2-norm throughout the domain. This has to be contrasted with the fac...

This study is concerned with the generation and propagation of strongly nonlinear waves in shallow water. A numerical wave flume developed where solitary cnoidal types are generated by use Level I Green-Naghdi (GN) equations a piston-type wavemaker. Waves GN theory enter domain fluid motion governed Navier–Stokes to achieve highest accuracy for propagation. The computations performed two dimens...

This paper focuses on the temporal and spatial evolutions of critical flow under unsteady rapidly varied conditions, which is defined based different viewpoints steady gradually conditions in classical fluid mechanics theory. So far, fundamental theory largely unknown for conditions. Taking a Gauss-type weir as an example, this work investigates comprehensively comparatively influences unsteadi...