Numerische Mathematik

, Volume 121, Issue 3, pp 397–431 | Cite as

A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems

Article

Abstract

The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L2 and the H1 norms are proved. The numerical solution obtained from the finite element method with quadrature formula is shown to be unique for a sufficiently fine mesh. The analysis is valid for both simplicial and rectangular finite elements of arbitrary order. Numerical experiments corroborate the theoretical convergence rates.

Mathematics Subject Classification (2000)

65N30 65M60 65D30 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Section de MathématiquesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.École Normale Supérieure de CachanBruzFrance

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