Numerical Solutions of Partial Differential Equations

  • Silvia Bertoluzza
  • Giovanni Russo
  • Silvia Falletta
  • Chi-Wang Shu

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Wavelets and Partial Differential Equations

    1. Front Matter
      Pages 1-1
    2. Pages 3-3
    3. Pages 5-21
    4. Back Matter
      Pages 55-57
  3. High-Order Shock-Capturing Schemes for Balance Laws

    1. Front Matter
      Pages 59-59
    2. Pages 61-81
    3. Pages 109-123
    4. Back Matter
      Pages 143-147
  4. Discontinuous Galerkin Methods: General Approach and Stability

About this book


This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical techniques.

The book has three parts. The first one is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of writing equivalent norms for the scale of Besov spaces allows to develop some new methods. The second part provides an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws, with emphasis on providing a unified view of such schemes by identifying the essential aspects of their construction. In the last part a general introduction is given to the discontinuous Galerkin methods for solving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates.


differential equation numerical analysis partial differential equation scientific computing wavelet

Authors and affiliations

  • Silvia Bertoluzza
    • 1
  • Giovanni Russo
    • 2
  • Silvia Falletta
    • 3
  • Chi-Wang Shu
    • 4
  1. 1.Istituto di Matematica Applicata eTecnologie Informatiche del C.N.R.Pavia
  2. 2.Dipartimento di Matematica ed InformaticaUniversità di CataniaCataniaItaly
  3. 3.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  4. 4.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information