mathematical foundation and applications of the p and hp finite element analysis

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mathematical foundation and applications of the p and hp finite element analysis

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mathematical foundation and applications of the p and hp finite element analysis

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title Mathematical Foundation and Applications of the P and H-P Finite Element Methods
authors Benqi Guo
publisher World Scientific Publishing Company Incorporated
publishedDate 2018-08-30
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.
pageCount 400
printType BOOK
categories Mathematics
maturityRating NOT_MATURE
panelizationSummary
language en
canonicalVolumeLink https://books.google.com/books/about/Mathematical_Foundation_and_Applications.html?hl=&id=7bDWPAAACAAJ

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