Chapter

Nonlinear Elliptic Equations

Rüdiger Verfürth

in A Posteriori Error Estimation Techniques for Finite Element Methods

Published in print April 2013 | ISBN: 9780199679423
Published online May 2013 | e-ISBN: 9780191758485 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199679423.003.0005

Series: Numerical Mathematics and Scientific Computation

Nonlinear Elliptic Equations

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We present a posteriori error estimates for nonlinear stationary problems departing from an abstract result which establishes the basic equivalence of error and residual. The main tool is the implicit function theorem along with modifications for bifurcation and turning points. We apply the abstract results to quasilinear elliptic equations and the stationary incompressible Navier–Stokes equations. The nonlinear approach also enables us to efficiently treat linear elliptic eigenvalue problems.

Keywords: quasilinear elliptic equations; eigenvalue problems; Navier–Stokes equations; implicit function theorem; bifucation; turning points

Chapter.  15435 words. 

Subjects: Applied Mathematics

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