© 2016

Advances in Discretization Methods

Discontinuities, Virtual Elements, Fictitious Domain Methods

  • Giulio Ventura
  • Elena Benvenuti


  • Presents advances in cutting-edge technologies for the numerical discretization of physical problems

  • Includes contributions from engineers and mathematicians alike

  • Pursues a more explanatory approach than classical journal papers


Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 12)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Enriched Methods for Flow and Mechanics in Heterogeneous Media

    1. Front Matter
      Pages 1-1
    2. Domenico Notaro, Laura Cattaneo, Luca Formaggia, Anna Scotti, Paolo Zunino
      Pages 3-25
    3. Bernd Flemisch, Alessio Fumagalli, Anna Scotti
      Pages 47-76
  3. Enhanced Finite Element Formulations for Fracture and Interface Problems

    1. Front Matter
      Pages 77-77
    2. Steffen Beese, Stefan Loehnert, Peter Wriggers
      Pages 79-102
    3. Ceren Gürkan, Esther Sala-Lardies, Martin Kronbichler, Sonia Fernández-Méndez
      Pages 103-122
    4. Yuan Jin, Olivier Pierard, Eric Wyart, Eric Béchet
      Pages 123-142
    5. Markus Schätzer, Thomas-Peter Fries
      Pages 143-164
  4. Polygonal and Polyhedral Methods

    1. Front Matter
      Pages 165-165
    2. Matías Fernando Benedetto, Stefano Berrone, Andrea Borio
      Pages 167-186
    3. Joe Collis, Paul Houston
      Pages 187-206
  5. Advances in XFEM/Fictitious Domain Methods

    1. Front Matter
      Pages 207-207
    2. Giulio Ventura, Claudia Tesei
      Pages 209-228
    3. Stefano Berrone, Andrea Bonito, Marco Verani
      Pages 229-244

About this book


This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.


Discontinuities Enriched approximations Virtual elements Fictitious domain Extended/generalized finite element method

Editors and affiliations

  • Giulio Ventura
    • 1
  • Elena Benvenuti
    • 2
  1. 1.Structural, Building, Geotechnical Eng.Politecnico di TorinoTorinoItaly
  2. 2.Department of EngineeringUniversity of FerraraFerraraItaly

Bibliographic information

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