Optimal Strong Error Estimates for Galerkin Finite Element Methods
This chapter contains our analysis of the strong error of convergence for Galerkin finite element approximation of stochastic evolution equation and is a slightly modified version of Kruse (IMA J. Numer. Anal., 2013). Our two main results in Sects. 3.4 an
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Raphael Kruse
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis (Zurich) Mario Di Bernardo (Bristol) Alessio Figalli (Pisa/Austin) Davar Khoshnevisan (Salt Lake City) Ioannis Kontoyiannis (Athens) Gabor Lugosi (Barcelona) Mark Podolskij (Heidelberg) Sylvia Serfaty (Paris and NY) Catharina Stroppel (Bonn) Anna Wienhard (Heidelberg)
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Raphael Kruse
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
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Raphael Kruse Department of Mathematics Bielefeld University Bielefeld, Germany
ISBN 978-3-319-02230-7 ISBN 978-3-319-02231-4 (eBook) DOI 10.1007/978-3-319-02231-4 Springer Cham Heidelberg New York Dordrecht London Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2013952955 Mathematics Subject Classification (2010): 65C30, 60H15, 65M60, 60H07, 35B65 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my love Christine
Preface
This monograph grew out of my Ph.D. thesis, which I wrote at Bielefeld Unive
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