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.
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© 2004 Springer Science+Business Media New York
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Ern, A., Guermond, JL. (2004). Coercive Problems. In: Theory and Practice of Finite Elements. Applied Mathematical Sciences, vol 159. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4355-5_3
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DOI: https://doi.org/10.1007/978-1-4757-4355-5_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1918-2
Online ISBN: 978-1-4757-4355-5
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