The anaerobic biodegradation mechanisms of linear alcohol ethoxylates (LAE) were studied in incubation experiments with anoxic sewage sludge. Sophisticated analytical techniques were applied, such as solid-phase extraction (SPE) followed by reversed phase high performance liquid chromatography (HPLC) procedures based on the derivatization of LAE and poly(ethylene glycol) (PEG). During the degradation of LAE C 12 (EO) ˜9, a technical dodecanol ethoxylate with an average of nine ethoxy (EO) units, and LAE C 12 (EO) 8 , a single ethoxymer, alcohol ethoxylates with shortened EO chains were released as the first identifiable metabolites, but no PEG products were observed. From our results it was concluded that the first step of anaerobic microbial attack on the LAE molecule is the cleavage of the terminal EO unit, releasing acetaldehyde stepwise, and shortening the ethoxy chain until the lipophilic moiety is reached. In contrast to the aerobic degradation pathway, where central scission prevails (the cleavage of the ether bond between alkyl and ethoxy chains), such a primary attack on the surfactant molecule is very unlikely in an anaerobic community of fermenting bacteria.

We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapidly at a microscopic scale. The multiscale method approximates the solution at the scale of interest at computational cost independent of the small scale by performing numerical upscaling (coupling of macro and micro finite element methods). Optimal a priori error estimates in the L 2 (H 1 ) and C 0 (L 2 ) norm are derived taking into account the error due to time discretization as well as macro and micro spatial discretizations. Further, we present numerical simulations to illustrate the theoretical error estimates and the applicability of the multiscale method to practical problems.

We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the microscopic scales. It can be interpreted as a linearized version of a standard nonlinear homogenization method. We prove the stability of the method and derive optimal a priori error estimates which are fully discrete in time and space. Numerical experiments confirm the error bounds and illustrate the efficiency of the method for various nonlinear problems.Keywords: monotone parabolic multiscale problem, linearized scheme, numerical homogenization method, fully discrete a priori error estimates.

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advectiondiffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection-diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domains within each macro element. The computational work involved is independent of the high oscillations in the problem at the smallest scale. The stability of our method (depending on both macro and micro mesh sizes) is established for both diffusion dominated and advection dominated regimes without any assumptions about the type of heterogeneities in the data. Fully discrete a priori error bounds are derived for locally periodic data. Numerical experiments confirm the theoretical error estimates.

We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapidly at a microscopic scale. The multiscale method approximates the homogenized solution at computational cost independent of the small scale by performing numerical upscaling (coupling of macro and micro finite element methods). Taking into account the error due to time discretization as well as macro and micro spatial discretizations, the convergence of the method is proved in the general L p (W 1,p ) setting. For p = 2, optimal convergence rates in the L 2 (H 1 ) and C 0 (L 2 ) norm are derived. Numerical experiments illustrate the theoretical error estimates and the applicability of the multiscale method to practical problems.

The aim of this paper is to discuss simulation methods of diffraction of electromagnetic waves on biperiodic structures. The region with complicated structures is discretised by Nédélec Finite Elements. In the unbounded homogeneous regions above and below, a plane wave expansion containing the exact far-field pattern is applied. A consistent coupling is achieved by the method of Nitsche. By numerical experiments we investigate the speed of convergence depending on the mesh refinement, the element order and the number of evanescent waves.

optimization-based numerical method for diffusion problems with sign-changing coefficients. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2017, 355 (4) AbstractA new optimization-based numerical method is proposed for the solution of diffusion problems with sign-changing conductivity coefficients. In contrast to existing approaches, our method does not rely on the discretization of a stabilized equation and the convergence of the scheme can be proved without any symmetry assumption on the mesh near the interface where the conductivity sign changes. RésuméUne méthode d'optimisation pour des problèmes de diffusion avec changement de signe. Nous proposons une nouvelle méthode, basée sur la résolution d'un problème de minimisation, pour l'approximation de problèmes de diffusion avec changement de signe. Cette approche, qui tire profit d'une reformulation du modèle initial sous la forme d'un problème de transmission, ne repose pas sur la discrétisation d'uneéquation stabilisée, et la convergence de la méthode est obtenue sans hypothèse de symétrie du maillage dans un voisinage de l'interface où la conductivité change de signe. Version française abrégéeDans cette note, nous introduisons une méthode d'optimisation pour l'approximation numérique de problèmes de diffusion dont la conductivité change de signe dans le domaine. La résolution numérique efficace de ce genre de problèmes est importante pour de nombreuses applications (e.g., super-lentilles, invisibilité), mais les méthodes existantes ne sont pour l'instant pas satisfaisantes. Dans [6], les deux approches envisagées reposent (i) sur la discrétisation d'uneéquation stabilisée, pour laquelle les taux de convergence obtenus sont sous-optimaux, ou (ii) sur des hypothèses de symétrie du maillage autour de l'interface où la conductivité change de signe, exigences pouvant s'avérer très contraignantes pour des interfaces générales (voir [3]) ou en 3D. La méthode numérique introduite ici, qui utilise une reformulation du modèle initial en un problème de transmission, ne repose pas sur l'ajout de dissipationà l'équation, et nous montrons sa convergence pour des problèmes elliptiques présentant un changement de signe sans aucune hypothèse de symétrie sur le maillage. Nous notons que cette méthode numérique a pour la première foisété introduite par Gunzburger et al. [9] (voir aussi [8]), dans un contexte de décomposition de domaine pour deséquations elliptiques classiques, sans preuve de convergence. L'application de cet algorithmeà des problèmes elliptiques présentant un changement de signe est introduite dans cette note, et la convergence de la méthode est démontrée.

This paper presents a new method for the generation of a beam finite element (FE) model from a three-dimensional (3D) data set acquired by micro-computed tomography (micro-CT). This method differs from classical modeling of trabecular bone because it models a specific sample only and differs from conventional solid hexahedron element-based FE approaches in its computational efficiency. The stress-strain curve, characterizing global mechanical properties of a porous structure, could be well predicted (R(2)=0.92). Furthermore, validation of the method was achieved by comparing local displacements of element nodes with the displacements directly measured by time-lapsed imaging methods of failure, and these measures were in good agreement. The presented model is a first step in modeling specific samples for efficient strength analysis by FE modeling. We believe that with upcoming high-resolution in-vivo imaging methods, this approach could lead to a novel and accurate tool in the risk assessment for osteoporotic fractures.