9780243091607 - Domain Decomposition and Iterative Refinement Methods for Mixed Finite Element Discretisations of Elliptic Problems (classic Reprint) by Tarek P. Mathew (3 results)
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Paperback. Condition: New. Print on Demand. This book explores iterative methods to solve saddle point linear systems, focusing on those derived from mixed finite element discretizations of elliptic Neumann problems using Raviart-Thomas elements. The book begins by establishing a theoretical framework. It then provides a proof o…f convergence of the iterative methods when applied to the mixed finite element case, showing that the rate of convergence is independent of the mesh parameter h. The book goes on to study algorithms involving subdomains with overlap, such as the classical Schwarz alternating method and the additive Schwarz method. It offers proofs of convergence for these iterative methods when applied to the mixed finite element case, again demonstrating that the rate of convergence is independent of h. Finally, the book examines a Dirichlet-Neumann algorithm for the mixed finite element case, providing a proof of convergence showing independence from h. The book concludes by discussing quantitative bounds for some many-level FAC algorithms. The author's insights are significant because they establish the convergence of iterative methods for solving saddle point linear systems arising from mixed finite element discretizations of elliptic Neumann problems, and they show that the rate of convergence is independent of the mesh parameter h. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.
