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Author: Glitzky, Annegret × Subject: heterostructures ×

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Now showing 1 - 3 of 3
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    Electro-reaction-diffusion systems in heterostructures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2000) Glitzky, Annegret; Hünlich, Rolf
    The paper is devoted to the mathematical investigation of a general class of electro-reaction-diffusion systems with nonsmooth data which arises in applications to semiconductor technology. Besides of a basic problem, a reduced problem is considered which is obtained if the kinetics of the free carriers is fast. For two dimensional domains we prove a global existence and uniqueness result. In addition, asymptotic properties of solutions are studied. Basic ideas are energy estimates, Moser iteration, regularization techniques and an existence result for electro-diffusion systems with weakly nonlinear volume and boundary source terms which is proved in the paper, too. The relationship between the property that the energy functional decays exponentially in time to its equilibrium value and the existence of global positive lower bounds for the densities of the species is investigated. We illustrate relations between the model and its reduced version in general and for concrete examples. Finally, we discuss the special features of heterostructures for simplified model problems.
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    Convergence of an implicit Voronoi finite volume method for reaction-diffusion problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fiebach, André; Glitzky, Annegret; Linke, Alexander
    We investigate the convergence of an implicit Voronoi finite volume method for reaction- diffusion problems including nonlinear diffusion in two space dimensions. The model allows to handle heterogeneous materials and uses the chemical potentials of the involved species as primary variables. The numerical scheme uses boundary conforming Delaunay meshes and preserves positivity and the dissipative property of the continuous system. Starting from a result on the global stability of the scheme (uniform, mesh-independent global upper and lower bounds), we prove strong convergence of the chemical activities and their gradients to a weak solution of the continuous problem. In order to illustrate the preservation of qualitative properties by the numerical scheme, we present a long-term simulation of the Michaelis-Menten-Henri system. Especially, we investigate the decay properties of the relative free energy and the evolution of the dissipation rate over several magnitudes of time, and obtain experimental orders of convergence for these quantities.
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    Uniform global bounds for solutions of an implicit Voronoi finite volume method for reaction-diffusion problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Fiebach, André; Glitzky, Annegret; Linke, Alexander
    We consider discretizations for reaction-diffusion systems with nonlinear diffusion in two space dimensions. The applied model allows to handle heterogeneous materials and uses the chemical potentials of the involved species as primary variables. We propose an implicit Voronoi finite volume discretization on regular Delaunay meshes that allows to prove uniform, mesh-independent global upper and lower L bounds for the chemical potentials. These bounds provide the main step for a convergence analysis for the full discretized nonlinear evolution problem. The fundamental ideas are energy estimates, a discrete Moser iteration and the use of discrete Gagliardo-Nirenberg inequalities. For the proof of the Gagliardo-Nirenberg inequalities we exploit that the discrete Voronoi finite volume gradient norm in 2d coincides with the gradient norm of continuous piecewise linear finite elements.