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

by Benqi (Univ Of Manitoba, Canada) Guo

Part of the Series In Analysis series

Hardback

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Description

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.