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Theory and practice of finite elements
Alexandre Ern,Jean-Luc Guermond +1 more
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Theoretical Foundations for Finite Element Interpolation and Banach Spaces by Galerkin Methods are given in this article, along with a discussion of the application of the Banach and Hilbert spaces in data-structuring and mesh generation.Abstract:
I Theoretical Foundations.- 1 Finite Element Interpolation.- 2 Approximation in Banach Spaces by Galerkin Methods.- II Approximation of PDEs.- 3 Coercive Problems.- 4 Mixed Problems.- 5 First-Order PDEs.- 6 Time-Dependent Problems.- III Implementation.- 7 Data Structuring and Mesh Generation.- 8 Quadratures, Assembling, and Storage.- 9 Linear Algebra.- 10 A Posteriori Error Estimates and Adaptive Meshes.- IV Appendices.- A Banach and Hilbert Spaces.- A.1 Basic Definitions and Results.- A.2 Bijective Banach Operators.- B Functional Analysis.- B.1 Lebesgue and Lipschitz Spaces.- B.2 Distributions.- B.3 Sobolev Spaces.- Nomenclature.- References.- Author Index.read more
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