Analysis of an anaerobic digestion model in landfill with mortality term

We study a mathematical model of anaerobic digestion with biomass recirculation, dedicated to landfill problems, and analyze its asymptotic behavior. We show that the global attractor is composed of an infinity of non-hyperbolic equilibria. For non-monotonic growth function, this feature has impacts on the performances of the bioprocess

The Science Question in Arab-Islamic Feminist Knowledge

Women's production of scientific feminist knowledge in Arab-Islamic society is rarely systematically addressed. The available literature reflects preconceptions and misconceptions about women's feminist scientific production of knowledge in the Arab world. In response to this, it is necessary to provide a systemic view of women's scientific production of knowledge in Arab-Islamic education and society. The focus then shifts from the 'woman question' in Arab- Islamic society to the more radical 'science question' in feminism, education and society in general

Optimal heat distributions by a gradient-based shape optimization method

In this paper, we consider the problem of locating coated inclusions in a 2D dimensional conductor material in order to obtain a suitable thermal environment. The mathematical model is described by elliptic partial differential equation with linear boundary condition, including heat transfer coefficient. A shape optimization problem is formulated by introducing a cost functional to solve the problem under consideration. The shape sensitivity analysis is rigorously performed for the problem by means of a Lagrangian formulation. The optimization problem is solved by means of gradient-based strategy and numerical experiments are carried out to demonstrate the feasibility of the approach

Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity

We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity. We study and implement discretizations based on such mixed finite element methods for the smooth domain formulations to the unilateral crack problems. We obtain convergence rates and optimal error estimates and we present some numerical experiments in agreement with the theoretical results

Mixed finite element methods for smooth domain formulation of crack problems

The discretization by finite element methods of a new variational formulation of crack problems is considered. The new formulation, called the smooth domain method, is derived for crack problems in the case of an elastic membrane. Inequality type boundary conditions are prescribed at the crack faces. The resulting model takes the form of an unilateral contact problem on the crack. We study and implement various mixed finite element methods for the numerical approximation of the model. A priori error estimates are derived and results of computations are provided. The convergence rates obtained from the numerical simulations are in agreement with the theoretical error estimates

An Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysis

Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain, all problems being coupled due to the nonlinear convection term. We propose a discretization of these equations which combines Fourier truncation and finite element methods applied to each two-dimensional system. We perform the a priori and a posteriori analysis of this discretization