Coercive Problems

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

Abstract

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.

Keywords

Bilinear Form Spectral Problem Discontinuous Galerkin Finite Element Approximation Finite Element Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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