This self-contained book describes 1D and 2D finite element codes and automatic hp-adaptivity strategies that are designed to deliver meshes in the full range of error levels. The book first considers standard 1D elliptic problems and a 1D wave propagation problem. It proceeds to discuss 2D elliptic problems, examining two model problems that are slightly beyond standard-level examples. The author also includes an entire chapter on geometric modeling and mesh generation. The book then focuses on 2D time-harmonic Maxwell equations. A companion CD-ROM containing 1D and 2D codes is included as...

With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code developed by the authors and their colleagues.
The first part of the book focuses on fundamentals of the 3D theory of hp methods as well as issues that arise when the code is...

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science.

This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces.

The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before...