Conforming finite element methods (FEMs)

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations

Published in print October 2010 | ISBN: 9780199577040
Published online January 2011 | e-ISBN: 9780191595172 | DOI:

Series: Numerical Mathematics and Scientific Computation

Conforming finite element methods (FEMs)

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This chapter considers the nowadays most important FEMs more extensively than the others. This chapter, on conforming FEMs, summarize the well-known approximation theory and extend it to specific smooth FEs. The ansatz and test functions satisfy the appropriate regularity and boundary conditions. The weak forms of linear and quasilinear problems are directly used to define conforming FEMs. Based upon Chapter 3, the proof of consistency, stability and convergence is pretty simple: Consistency is nearly obvious for the conforming FEMs here and the wavelets in Chapter 9. Stability is proved by compactly perturbing the coercive principal parts, or, for the Navier-Stokes problem, the Stokes operator.

Keywords: approximation theory for Fes; conforming FEMs; consistency obvious; stability by compactly; coercive principal parts

Chapter.  23887 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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