Coercive Problems

  • Alexandre Ern
  • Jean-Luc Guermond
Part of the Applied Mathematical Sciences book series (AMS, volume 159)


This chapter deals with problems whose weak formulation is endowed with a coercivity property. The key examples investigated henceforth are scalar elliptic PDEs, spectral problems associated with the Laplacian, and PDE systems derived from continuum mechanics. The goal is twofold: First, to set up a mathematical framework for well-posedness; then, to investigate conformal and non-conformal finite element approximations based on Galerkin methods. Error estimates are derived from the theoretical results of Chapters 1 and 2 and are illustrated numerically. The last section of this chapter is concerned with coercivity loss and is meant to be a transition to Chapters 4 and 5.


Bilinear Form Spectral Problem Discontinuous Galerkin Finite Element Approximation Finite Element Space 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Alexandre Ern
    • 1
  • Jean-Luc Guermond
    • 2
  1. 1.CERMICS, ENPCMarne la Vallée cedex 2France
  2. 2.LIMSI, CNRSOrsay cedexFrance

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