Mathematical Foundation And Applications Of The P And H-p Finite Element Methods

Benqi Guo (Autor)

Buch | Hardcover

400 Seiten

2018
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-283-893-3 (ISBN)

Infos

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 Babuska-Guo-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.

Produkt-Details

• Erscheint lt. Verlag: 30.8.2018
• Reihe/Serie: Series In Analysis ; 4
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 981-283-893-7 / 9812838937
• ISBN-13: 978-981-283-893-3 / 9789812838933
• Zustand: Neuware