Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs

This book is a comprehensive textbook suitable for graduate coursework, professional engineering, and academic research, divided into short chapters with exercises and solutions. It covers elliptic and mixed PDEs, including approximation techniques, and applies them to various problems. The appendix provides results on linear operators in Banach spaces.

Format: Paperback / softback
Length: 492 pages
Publication date: 23 April 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook serves as the second installment of a three-part series designed for advanced study, professional engineering practice, and academic research. It is also well-suited for graduate flipped courses. Each volume in the series is thoughtfully structured into concise chapters, making it convenient for teaching purposes. Each chapter can be effectively covered in a single teaching session, accompanied by comprehensive exercises and solutions accessible through a dedicated website. The text employs a lively blend of examples, fundamental concepts, rigorous proofs, and insightful references to the literature to foster scientific literacy.

Volume II is organized into 32 chapters, along with an appendix. The first part of the volume delves into the approximation of elliptic and mixed partial differential equations (PDEs), commencing with foundational results on well-posed weak formulations and their approximation through the Galerkin method. The topics covered encompass essential findings such as the BNB theorem, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Additionally, important implementation considerations related to quadratures, linear algebra, and assembly are addressed.

The remaining chapters of Volume II are dedicated to PDEs that possess a coercivity property. This section explores conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix-Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to a wide range of PDEs, including elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows).

In conclusion, this textbook offers a valuable resource for advanced students, professionals, and researchers in the field of partial differential equations. Its comprehensive coverage, engaging writing style, and extensive exercises and solutions make it an essential tool for advancing knowledge and understanding in this complex subject area.

Weight: 856g
Dimension: 154 x 234 x 27 (mm)
ISBN-13: 9783030569242
Edition number: 1st ed. 2021