Mathematical Foundation And Applications Of The P And H-p Finite Element Methods
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A01=Benqi Guo
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Approximation Theory
Author_Benqi Guo
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Babuska-Guo-Weighted Sobolev Space
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Exponential Convergence
Jacobi-Weighted Sobolev and Besov Spaces
Language_English
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P and H-P Finite Element Method
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SN=Series In Analysis
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Product details
- ISBN 9789812838933
- Publication Date: 30 Aug 2018
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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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.
