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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

  • The authors are the leading experts in the field. It is hard to find such a selected list of authors writing about the developments they are carrying out at present
  • The main developments in recent approaches to numerical PDEs are gathered in this book
  • The survey nature of each contribution makes the volume an ideal reading for practitioners, academics, as well as graduate students wishing to grasp the fundamental aspect of modern numerical PDE approaches

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 114)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-viii
  2. Virtual Element Implementation for General Elliptic Equations

    • Lourenco Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini, Alessandro Russo
    Pages 39-71
  3. On Quasi-Interpolation Operators in Spline Spaces

    • Annalisa Buffa, Eduardo M. Garau, Carlotta Giannelli, Giancarlo Sangalli
    Pages 73-91
  4. Robust DPG Methods for Transient Convection-Diffusion

    • Truman Ellis, Jesse Chan, Leszek Demkowicz
    Pages 179-203
  5. A Survey of Trefftz Methods for the Helmholtz Equation

    • Ralf Hiptmair, Andrea Moiola, Ilaria Perugia
    Pages 237-279
  6. Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains

    • Paola F. Antonietti, Andrea Cangiani, Joe Collis, Zhaonan Dong, Emmanuil H. Georgoulis, Stefano Giani et al.
    Pages 281-310
  7. Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes

    • Konstantin Lipnikov, Gianmarco Manzini
    Pages 311-342
  8. Foundations of the MHM Method

    • Christopher Harder, Frédéric Valentin
    Pages 401-433
  9. Erratum to: A Survey of Trefftz Methods for the Helmholtz Equation

    • Ralf Hiptmair, Andrea Moiola, Ilaria Perugia
    Pages E1-E1
  10. Back Matter

    Pages 435-442

About this book

This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches.


The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

Editors and Affiliations

  • Department of Mathematics & Statistics, University of Strathclyde, Glasgow, United Kingdom

    Gabriel R. Barrenechea

  • Istituto di Matematica Applicata e Tecnologie Informatiche - Pavia, Consiglio Nazionale delle Ricerche, Pavia, Italy

    Franco Brezzi

  • Department of Mathematics, University of Leicester, Leicester, United Kingdom

    Andrea Cangiani

  • Department of Mathematics, National Technical University of Athens, Zografou, Greece

    Emmanuil H. Georgoulis

Bibliographic Information

  • Book Title: Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

  • Editors: Gabriel R. Barrenechea, Franco Brezzi, Andrea Cangiani, Emmanuil H. Georgoulis

  • Series Title: Lecture Notes in Computational Science and Engineering

  • DOI: https://doi.org/10.1007/978-3-319-41640-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-41638-0Published: 04 October 2016

  • Softcover ISBN: 978-3-319-82402-4Published: 15 June 2018

  • eBook ISBN: 978-3-319-41640-3Published: 03 October 2016

  • Series ISSN: 1439-7358

  • Series E-ISSN: 2197-7100

  • Edition Number: 1

  • Number of Pages: VIII, 433

  • Number of Illustrations: 19 b/w illustrations, 21 illustrations in colour

  • Topics: Computational Science and Engineering, Partial Differential Equations

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access