In this article, we propose a novel discontinuous Galerkin method for convection-diffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable and competitive with the main existing methods for these problems. The second is that, when the method uses polynomial… (More)
In this article, we discuss the numerical approximation of transport phenomena occurring at material interfaces between physical subdomains with heterogenous properties. The model in each subdomain consists of a partial differential equation with diffusive, convective and reactive terms, the coupling between each subdomain being realized through an… (More)
This article deals with the analysis of the functional iteration, denoted Generalized Gummel Map (GGM), proposed in  for the decoupled solution of the Quantum Drift–Diffusion (QDD) model. The solution of the problem is characterized as being a fixed point of the GGM, which permits the establishment of a close link between the theoretical existence… (More)
We present a Discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG)) which is based on introducing variables defined in the interior… (More)
In this work we present a mathematical model for the coupling between biomechanics and hemodynamics in the lamina cribrosa, a thin porous tissue at the base of the optic nerve head which is thought to be the site of injury in ocular neurodegenerative diseases such as glaucoma. In this exploratory two-dimensional investigation, the lamina cribrosa is modeled… (More)
A unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the Her-rmann formulation within the Hellinger-Reissner principle. This quasi-optimally converging extension of PEERS (Plane Elasticity Element with Reduced Symmetry) is called Dual-Mixed Hybrid formulation (DMH). Explicit… (More)
We report about two specific breakthroughs, relevant to the mathematical modeling and numerical simulation of tissue growth in the context of cartilage tissue engineering in vitro. The proposed models are intended to form the building blocks of a bottom-up multiscale analysis of tissue growth, the idea being that a full microscale analysis of the construct,… (More)
We consider a convection–diffusion–reaction problem, and we analyze a stabilized mixed finite volume scheme introduced in . The scheme is presented in the format of Discontinuous Galerkin methods, and error bounds are given, proving O(h 1/2) convergence in the L 2-norm for the scalar variable, which is approximated with piecewise constant elements.