Méthodes non conformes pour des équations aux dérivées partielles avec diffusion

Abstract : This manuscript contains a resume of my work after my PhD thesis. In recent years I considered some issues related to the discretization of problems stemming from different areas in fluid mechanics. The common element is the presence of diffusive terms modeled by second order differential operators. For different reasons I was led to consider non-conforming methods, i.e. methods based on discrete spaces that are not contained in the continuous space naturally associated with the weak formulation of the problem. More specifically, two main families of methods are considered herein, that is to say, discontinuous Galerkin and finite volume methods. The material is organized as follows. Chapters 1–3 provide general information including a curriculum vitæ and the full list of publications. Chapters 4–5 contain an extended summary of my work. Specifically, Chapter 4 is devoted to discontinuous Galerkin methods, while Chapter 5 deals with finite volume methods. Although the focus is generally on motivations, details are provided when necessary to provide additional information or to indicate future lines of research. Appendix A contains the abstracts of the PhD theses currently under my supervision. Finally, a complete bibliography counting over 250 entries is provided. For ease of reading, my publications are cited using a progressive number, while articles from the general bibliography are referenced using the initials of the authors.
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Submitted on : Friday, December 24, 2010 - 5:02:17 PM
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Daniele Antonio Di Pietro. Méthodes non conformes pour des équations aux dérivées partielles avec diffusion. Mathématiques [math]. Université Paris-Est, 2010. ⟨tel-00550230⟩

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