Mathematical Foundation and Applications of the P and H-P Finite Element Methods
by Benqi Guo (9789812838933)

Mathematical Foundation and Applications of the P and H-P Finite Element Methods
 

Benqi Guo


Release Date: 01 September 2009
Format: Hardback
Pages: 400
Category: Mathematical Analysis
Publisher: World Scientific Publishing Company
ISBN: 9789812838933
ISBN-10: 9812838937



This book provides comprehensive knowledge and up-to-date developments of the p and h-p finite element methods. Introducing systematically the Jacobi-weighted Sobolev and Besov spaces, it establishes the approximation theory in the framework of these spaces in n dimensions. This is turn leads to the optimal convergence of the p and h-p finite element methods with quasi-uniform meshes in two dimensions for problems with smooth solutions and singular solutions on polygonal domains.

The book is based on the author's research on the p and h-p finite element methods over the past three decades. This includes the recently established approximation theory in Jacobi-weighted Sobolev and Besov spaces and rigorous proof of the optimal convergence of the p and h-p finite element method with quasi-uniform meshes for elliptic problems on polygonal domains. Indeed, these have now become the mathematical foundation of the high-order finite/boundary element method. In addition, the regularity theory in the countably BabuskaGuo-weighted Sobolev spaces, which the author established in the mid-1980s, provides a unique mathematical foundation for the h-p finite element method with geometric meshes and leads to the exponential rate of convergence for elliptic problems on polygonal domains.

AUD $180.95

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