© 2018

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017

  • Tom Lyche
  • Carla Manni
  • Hendrik Speleers
  • Contains a multi-perspective exposition of the use of splines in the numerical treatment of PDEs

  • Covers mathematical foundations, numerical paradigms, and implementational issues

  • Collects contributions from internationally renowned experts in the field


Part of the Lecture Notes in Mathematics book series (LNM, volume 2219)

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2219)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Thomas J. R. Hughes, Giancarlo Sangalli, Mattia Tani
    Pages 237-315
  3. Back Matter
    Pages 317-318

About this book


This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. 

A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. 

The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.


Adaptive Multiscale Methods Isogeometric Analysis Numerical Treatment of PDEs Spectral Analysis Spline Approximation

Authors and affiliations

  1. 1.Mathematical InstituteUniversity of CologneCologneGermany
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Department of MathematicsUniversity of PaviaPaviaItaly
  4. 4.Department of Science and High TechnologyUniversity of InsubriaComoItaly

Editors and affiliations

  • Tom Lyche
    • 1
  • Carla Manni
    • 2
  • Hendrik Speleers
    • 3
  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Department of MathematicsUniversity of Rome Tor VergataROMAItaly
  3. 3.Department of MathematicsUniversity of Rome Tor VergataROMAItaly

About the editors

To be Provided.

Bibliographic information

  • Book Title Splines and PDEs: From Approximation Theory to Numerical Linear Algebra
  • Book Subtitle Cetraro, Italy 2017
  • Authors Angela Kunoth
    Tom Lyche
    Giancarlo Sangalli
    Stefano Serra-Capizzano
  • Editors Tom Lyche
    Carla Manni
    Hendrik Speleers
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-94910-9
  • eBook ISBN 978-3-319-94911-6
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages IX, 318
  • Number of Illustrations 11 b/w illustrations, 51 illustrations in colour
  • Topics Numerical Analysis
    Approximations and Expansions
    Partial Differential Equations
  • Buy this book on publisher's site
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