The present work concerns the numerical approximation of the $M_1$ model for radiative transfer. The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this model. We propose to derive an HLLC method which preserves the stationary contact waves. To supplement this essential property, the method is proved to be robust and to preserve the physical admissible states. Next, a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical regimes. The relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system is studied when the fluid flow within the channel is induced due to the impulsive movement of the one of the plates of the channel. The plates of the channel are considered porous and the magnetic field is fixed relative to the moving plate. Exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate is also obtained. Asymptotic behaviour of the solution is analyzed for small as well as large values of time $t$ to highlight the transient approach to the final steady state flow and the effects of rotation, magnetic field and suction/injection. It is found that suction has retarding influence on the primary as well as secondary flow where as injection and time have accelerating influence on the primary and secondary flows.

Discontinuous Galerkin methods as a solution technique of second order elliptic problems, have been increasingly exploited by several authors in the past ten years. It is generally claimed the alledged attractive geometrical flexibility of these methods, although they involve considerable increase of computational effort, as compared to continuous methods. This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic $m$-harmonic equations in a bounded domain of $\mathbb{R}^n$, for $n$ = 2 or $n$ = 3, with $m $$\geq$$ n+1$, as a valid and reasonable alternative to classical finite elements, or even to boundary element methods.

In this paper, an energy-compatibility condition is used for stress optimization in the derivation of new accurate 8-node hexahedral elements for three-dimensional elasticity. Equivalence of the proposed hybrid method to an enhanced strains method is established, which makes it easy to extend the method to general nonlinear problems. Numerical tests show that the resultant elements possess high accuracy at coarse meshes, are insensitive to mesh distortions and free from volume locking in the analysis of beams, plates and shells.

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation. A non linear electro-elastic constitutive law is used to model the piezoelectric material. The unilateral contact is modelled using the Signorini condition, nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition. Existence and uniqueness of a weak solution is established. The finite elements approximation of the problem is presented. A priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.

In this paper, we apply Ma's variation of parameters method (VPM) for solving Fisher's equations. The suggested algorithm proved to be very efficient and finds the solution without any discretization, linearization, perturbation or restrictive assumptions. Numerical results reveal the complete reliability of the proposed VPM.

Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This paper deals with the lateral-torsional buckling of elastic nonlocal small-scale beams. Eringen's model is chosen for the nonlocal constitutive bending-curvature relationship. The effect of prebuckling deformation is taken into consideration on the basis of the Kirchhoff-Clebsch theory. It is shown that the application of Eringen's model produces small-length scale terms in the nonlocal elastic lateral-torsional buckling moment of a hinged-hinged strip beam. Clearly, the non-local parameter has the effect of reducing the critical lateral-torsional buckling moment. This tendency is consistent with the one observed for the in-plane stability analysis, for the lateral buckling of a hinged-hinged axially loaded column. The lateral buckling solution can be derived from a physically motivated variational principle.