Finite Elements Ii
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Finite Elements II
This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
Finite Elements 1-2-3
This text is intended for the student who is being introduced for the first time to the Finite Element Method (FEM). Written in a simple, easy to follow manner, the book is a practical guide for learning the basics of the method and applying them to a wide variety of problems. The book focuses on the practical applications of fundamental concepts, with special emphasis on fluid mechanics. Computational experiments are integrated throughout the text via example problems and exercises. A comprehensive finite element instructional computer code, written for the PC using standard FORTRAN 77, is used to support every basic step and solve the set of example problems. The coverage of numerical linear algebra presents a unique numerical scheme based on continuing finite element/finite difference methodologies.
Theory and Practice of Finite Elements
Author: Alexandre Ern
language: en
Publisher: Springer Science & Business Media
Release Date: 2004-04-29
This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.