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at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial diierential equations of hyper-bolic type, developing shock discontinuities. The lectures were given by four outstanding scientists in the eld and reeect the state of the art of a broad spectrum of topics. The most modern and(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)
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)
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 propose a unified framework for Quantum–Corrected Drift–Diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical Drift–Diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum–correction to the electric(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)
A new family of Petrov-Galerkin nite element methods on triangular grids is constructed for singularly perturbed elliptic problems in two dimensions. It uses divergence-free trial functions that form a natural generalization of one-dimensional exponential trial functions. This family includes an improved version of the divergence-free nite element method(More)