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.
- ISBN10 9812838945
- ISBN13 9789812838940
- Publish Date July 2009
- Publish Status Active
- Publish Country SG
- Imprint World Scientific Publishing Co Pte Ltd
- Format Hardcover
- Pages 400
- Language English