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Advances in Discretization Methods

Discontinuities, Virtual Elements, Fictitious Domain Methods

  • Book
  • © 2016

Overview

Editors:
  1. Giulio Ventura

    1. Structural, Building, Geotechnical Eng., Politecnico di Torino, Torino, Italy

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  2. Elena Benvenuti

    1. Department of Engineering, University of Ferrara, Ferrara, Italy

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    You can also search for this editor in PubMed   Google Scholar

  • 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 book series: SEMA SIMAI Springer Series (SEMA SIMAI, volume 12)

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Table of contents (12 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. A Mixed Finite Element Method for Modeling the Fluid Exchange Between Microcirculation and Tissue Interstitium

      • Domenico Notaro, Laura Cattaneo, Luca Formaggia, Anna Scotti, Paolo Zunino
      Pages 3-25

    3. On a PDE-Constrained Optimization Approach for Flow Simulations in Fractured Media

      • Sandra Pieraccini, Stefano Scialò
      Pages 27-45

    4. A Review of the XFEM-Based Approximation of Flow in Fractured Porous Media

      • 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
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    2. Modeling of Fracture in Polycrystalline Materials

      • Steffen Beese, Stefan Loehnert, Peter Wriggers
      Pages 79-102

    3. eXtended Hybridizable Discontinuous Galerkin (X-HDG) for Void and Bimaterial Problems

      • Ceren Gürkan, Esther Sala-Lardies, Martin Kronbichler, Sonia Fernández-Méndez
      Pages 103-122

    4. Crack Lip Contact Modeling Based on Lagrangian Multipliers with X-FEM

      • Yuan Jin, Olivier Pierard, Eric Wyart, Eric Béchet
      Pages 123-142

    5. Stress Intensity Factors Through Crack Opening Displacements in the XFEM

      • Markus Schätzer, Thomas-Peter Fries
      Pages 143-164

  4. Polygonal and Polyhedral Methods

    1. Front Matter

      Pages 165-165
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    2. The Virtual Element Method for Underground Flow Simulations in Fractured Media

      • Matías Fernando Benedetto, Stefano Berrone, Andrea Borio
      Pages 167-186

    3. Adaptive Discontinuous Galerkin Methods on Polytopic Meshes

      • Joe Collis, Paul Houston
      Pages 187-206

  5. Advances in XFEM/Fictitious Domain Methods

    1. Front Matter

      Pages 207-207
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    2. Stabilized X-FEM for Heaviside and Nonlinear Enrichments

      • Giulio Ventura, Claudia Tesei
      Pages 209-228

    3. An Adaptive Fictitious Domain Method for Elliptic Problems

      • Stefano Berrone, Andrea Bonito, Marco Verani
      Pages 229-244

    4. Higher-Order Accurate Integration for Cut Elements with Chen-Babuška Nodes

      • Thomas-Peter Fries
      Pages 245-269
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Keywords

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.

Editors and Affiliations

  • Structural, Building, Geotechnical Eng., Politecnico di Torino, Torino, Italy

    Giulio Ventura

  • Department of Engineering, University of Ferrara, Ferrara, Italy

    Elena Benvenuti

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