Open AccessBook
Mixed and Hybrid Finite Element Methods
Franco Brezzi,Michel Fortin +1 more
TLDR
Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.Abstract:
Variational Formulations and Finite Element Methods. Approximation of Saddle Point Problems. Function Spaces and Finite Element Approximations. Various Examples. Complements on Mixed Methods for Elliptic Problems. Incompressible Materials and Flow Problems. Other Applications.read more
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Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
TL;DR: In this paper, a framework for the analysis of a large class of discontinuous Galerkin methods for second-order elliptic problems is provided, which allows for the understanding and comparison of most of the discontinuous methods that have been proposed over the past three decades.
Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
Journal ArticleDOI
Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
TL;DR: In this paper, an approach is developed for deriving variational methods capable of representing multiscale phenomena, which leads to the well-known Dirichlet-to-Neumann formulation.
Journal ArticleDOI
deal.II—A general-purpose object-oriented finite element library
TL;DR: The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools.
Book
Shape optimization by the homogenization method
TL;DR: In this article, a relaxed formulation for shape optimization in the context of shape optimization is presented, where the authors seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading.