Dimensional model reduction for flow through fractures in poroelastic media

We study the interaction between a poroelastic medium and a fracture filled with fluid. The flow in the fracture is described by the Brinkman equations for an incompressible fluid and the poroelastic medium by the quasi-static Biot model. The two models are fully coupled via the kinematic and dynamic conditions. The Brinkman equations are then averaged over the cross-sections, giving rise to a reduced flow model on the fracture midline. We derive suitable interface and closure conditions between the Biot system and the dimensionally reduced Brinkman model that guarantee solvability of the resulting coupled problem. We design and analyze a numerical discretization scheme based on finite elements in space and the Backward Euler in time, and perform numerical experiments to compare the behavior of the reduced model to the full-dimensional formulation and study the response of the model with respect to its parameters

The Effect of Hypoallergenic Diagnostic Diet in Adolescents and Adult Patients Suffering from Atopic Dermatitis

Aim: To evaluate the effect of a diagnostic hypoallergenic diet on the severity of atopic dermatitis in patients over 14 years of age. Materials and Methods: The diagnostic hypoallergenic diet was recommended to patients suffering from atopic dermatitis for a period of 3 weeks. The severity of atopic dermatitis was evaluated at the beginning and at the end of this diet (SCORAD I, SCORAD II) and the difference in the SCORAD over this period was statistically evaluated. Results: One hundred and forty-nine patients suffering from atopic dermatitis were included in the study: 108 women and 41 men. The average age of the subjects was 26.03 (SD: 9.6 years), with the ages ranging from a minimum of 14 years to a maximum of 63 years. The mean SCORAD at the beginning of the study (SCORAD I) was 32.9 points (SD: 14.1) and the mean SCORAD at the end of the diet (SCORAD II) was 25.2 points (SD: 9.99). The difference between SCORAD I and SCORAD II was evaluated with the Wilcoxon signed-rank test. The average decrease of SCORAD was 7.7 points, which was statistically significant (P=.00000). Conclusion: Introduction of the diagnostic hypoallergenic diet may serve as a temporary medical solution" in patients suffering from moderate or severe forms of atopic dermatitis. It is recommended that this diet be used in the diagnostic workup of food allergy

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(\Omega; \Gamma)$ of $H^1(\Omega)$-functions with $H^1(\Gamma)$-traces, where $\Gamma \subseteq \partial \Omega$. Based on a variational method, we prove that the solution of the generalized Robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard Robin problem. We numerically solve generalized Robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space $H^1(\Omega; \Gamma)$