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

  • Book
  • © 2016

Overview

Editors:
  1. Gabriel R. Barrenechea

    1. Department of Mathematics & Statistics, University of Strathclyde, Glasgow, United Kingdom

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  2. Franco Brezzi

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

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  3. Andrea Cangiani

    1. Department of Mathematics, University of Leicester, Leicester, United Kingdom

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  4. Emmanuil H. Georgoulis

    1. Department of Mathematics, National Technical University of Athens, Zografou, Greece

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  • 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
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  2. Numerical Homogenization Methods for Parabolic Monotone Problems

    • Assyr Abdulle
    Pages 1-38

  3. Virtual Element Implementation for General Elliptic Equations

    • Lourenco Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini, Alessandro Russo
    Pages 39-71

  4. On Quasi-Interpolation Operators in Spline Spaces

    • Annalisa Buffa, Eduardo M. Garau, Carlotta Giannelli, Giancarlo Sangalli
    Pages 73-91

  5. Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

    • Erik Burman
    Pages 93-127

  6. Static Condensation, Hybridization, and the Devising of the HDG Methods

    • Bernardo Cockburn
    Pages 129-177

  7. Robust DPG Methods for Transient Convection-Diffusion

    • Truman Ellis, Jesse Chan, Leszek Demkowicz
    Pages 179-203

  8. A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods

    • Daniele A. Di Pietro, Alexandre Ern, Simon Lemaire
    Pages 205-236

  9. A Survey of Trefftz Methods for the Helmholtz Equation

    • Ralf Hiptmair, Andrea Moiola, Ilaria Perugia
    Pages 237-279

  10. 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

  11. Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes

    • Konstantin Lipnikov, Gianmarco Manzini
    Pages 311-342

  12. Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors

    • Daniel Peterseim
    Pages 343-369

  13. Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods

    • Chi-Wang Shu
    Pages 371-399

  14. Foundations of the MHM Method

    • Christopher Harder, Frédéric Valentin
    Pages 401-433

  15. Erratum to: A Survey of Trefftz Methods for the Helmholtz Equation

    • Ralf Hiptmair, Andrea Moiola, Ilaria Perugia
    Pages E1-E1

  16. Back Matter

    Pages 435-442
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Keywords

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

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