Overview

This book deals with the adaptive numerical solution of parabolic partial differential equations (PDEs) arising in many branches of applications. It illustrates the interlocking of numerical analysis, the design of an algorithm and the solution of practical problems. In particular, a combination of Rosenbrock-type one-step methods and multilevel finite elements is analysed. Implementation and efficiency issues are discussed. Special emphasis is put on the solution of real-life applications that arise in today's chemical industry, semiconductor-device fabrication and health care. The book is intended for graduate students and researchers who are either interested in the theoretical understanding of instationary PDE solvers or who want to develop computer codes for solving complex PDEs.

Full Product Details

Author:   Jens Lang
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 2001
Volume:   16
Dimensions:   Width: 15.50cm , Height: 1.00cm , Length: 23.50cm
Weight:   0.307kg
ISBN:  

9783642087479

ISBN 10:   3642087477
Pages:   162
Publication Date:   07 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

I Introduction.- II The Continuous Problem and Its Discretization in Time.- III Convergence of the Discretization in Time and Space.- IV Computational Error Estimation.- V Towards an Effective Algorithm. Practical Issues.- VI Illustrative Numerical Tests.- VII Applications from Computational Sciences.- Appendix A. Advanced Tools from Functional Analysis.- §1. Gelfand Triple.- §2. Sesquilinear Forms and Bounded Operators in Hilbert Spaces.- §3. Unbounded Operators in Hilbert Spaces.- §4. Analytic Semigroups.- §5. Vectorial Functions Defined on Real Intervals.- Appendix B. Consistency and Stability of Rosenbrock Methods.- §1. Order Conditions.- §2. The Stability Function.- §3. The Property ‘Stiffly Accurate’.- Appendix C. Coefficients of Selected Rosenbrock Methods.- Appendix D. Color Plates.- Table of Notations.

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