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We propose and analyze a symmetric weighted interior penalty (SWIP) method to approximate in a Discontinuous Galerkin framework advection-diffusion equations with anisotropic and discontinuous diffusivity. The originality of the method consists in the use of diffusivity-dependent weighted averages to better cope with locally small diffusivity (or(More)
We propose a domain decomposition method for advection-diffusion-reaction equations based on Nitsche's transmission conditions. The ad-vection dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries. We prove the convergence of the finite element solutions of the discrete problem(More)
A Discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally vanishing and anisotropic diffusivity We consider Discontinuous Galerkin approximations of advection-diffusion equations with anisotropic and discontinuous diffusivity, and propose the symmetric weighted interior penalty (SWIP) method. The originality of(More)
Mathematical models and numerical methods have emerged as fundamental tools in the investigation of life sciences. In particular, this is the case of medical devices as cardiovascular drug eluting stents where experimental/clinical evidence may often be very expensive and extremely variable. Here we present a complete overview of mathematical models and(More)
Model reduction strategies enable computational analysis of controlled drug release from cardiovascular stents. Abstract Medicated cardiovascular stents, also called drug eluting stents (DES) represent a relevant application of controlled drug release mechanisms. Modeling of drug release from DES also represents a challenging problem for theoretical and(More)
We develop and analyze a Discontinuous Galerkin (DG) method based on weighted interior penalties (WIP) applied to second order PDEs and in particular to advection-diffusion-reaction equations featuring non-smooth and possibly vanishing diffusivity. First of all, looking at the derivation of a DG scheme with a bias to domain decomposition methods, we(More)