Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity

We study the solvability and Galerkin approximation of an exterior hyperelastic interface problem arising in plane elasticity. The weak formulation is obtained from an appropriate combination of a mixed finite element approach with a Dirichlet-to-Neumann method. The derivation of our results is based on some tools from nonlinear functional analysis and the Babuska-Brezzi theory for variational problems with constraints.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Relaxing the hypotheses of Bielak–MacCamy’s BEM–FEM coupling

In this paper we show that the quasi-symmetric coupling of finite and boundary elements of Bielak and MacCamy can be freed of two very restricting hypotheses that appeared in the original paper: the coupling boundary can be taken polygonal/polyhedral and coupling can be done using the normal stress instead of the pseudostress. We will do this by first considering a model problem associated to the Yukawa equation, where we prove how compactness arguments can be avoided to show stability of Galerkin discretizations of a coupled system in the style of Bielak–MacCamy’s. We also show how discretization properties are robust in the continuation parameter that appears in the formulation. This analysis is carried out using a new and very simplified proof of the ellipticity of the Johnson–Nédélec BEM–FEM coupling operator. Finally, we show how to apply the techniques that we have fully developed in the model problem to the linear elasticity system.     

Changing the adsorption capacity of coal-based honeycomb monoliths for pollutant removal from liquid streams by controlling their porosity

Coal-based honeycomb monoliths extruded using methods developed for ceramic materials have been used to retain methylene blue and p-nitrophenol from aqueous solutions. The influence of the filters’ thermal treatment on their textural properties and performance as adsorbents was examined. Characterization by N₂ physisorption, mercury porosimetry and scanning electron microscopy along with adsorption tests under dynamic conditions suggest that, depending on the pollutant and its initial concentration, it can be more convenient to previously submit the monoliths to a simple carbonization or to an additional activation, with or without preoxidation, as a consequence of their different resulting pore structures. Infrared spectroscopy indicates that their different adsorption behaviour seems not to be related to differences in their surface chemical groups. In addition, axial crushing tests show that the monoliths have an acceptable mechanical resistance for the application investigated.     

Possible one-dimensional 3He quantum fluid formed in nanopores

Heat capacity measurements have been made down to 5 mK for 3He fluid films adsorbed in one-dimensional (1D) nanometer-scale pores, 28 A in diameter, preplated with 4He of 1.47 atomic layers. At low 3He density, the heat capacity shows a density-dependent, Schottky-like peak near 150 mK asymptoting to the value corresponding to a 2D Boltzmann gas at high temperatures. The peak behavior is attributed to the crossover from a 2D gas to a 1D state at low temperatures. The degenerate state of the 1D 3He fluid is indicated by a predominantly linear temperature dependence below about 30 mK.     

A domain decomposition method for linear exterior boundary value problems

In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity. We first use a Dirichlet-to-Neumann mapping, derived from boundary integral equation methods, to transform the exterior problem into an equivalent mixed boundary value problem on a bounded domain. This domain is decomposed into a finite number of annular subregions, and the Dirichlet data on the interfaces is introduced as the unknown of the associated Steklov-Poincaré problem. This problem is solved with the Richardson method by introducing a Dirichlet-Robin-type preconditioner, which yields an iteration-by-subdomains algorithm well suited for parallel computations. The corresponding analysis for the finite element approximations and some numerical experiments are also provided.