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Numerische Mathematik

, Volume 132, Issue 3, pp 433–462 | Cite as

Intrinsic finite element methods for the computation of fluxes for Poisson’s equation

  • P. G. Ciarlet
  • P. CiarletJrEmail author
  • S. A. Sauter
  • C. Simian
Article

Abstract

In this paper we consider an intrinsic approach for the direct computation of the fluxes for problems in potential theory. We develop a general method for the derivation of intrinsic conforming and non-conforming finite element spaces and appropriate lifting operators for the evaluation of the right-hand side from abstract theoretical principles related to the second Strang Lemma. This intrinsic finite element method is analyzed and convergence with optimal order is proved.

Keywords

Elliptic boundary value problems Conforming and non-conforming finite element spaces Intrinsic formulation 

Mathematics Subject Classification

65N30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • P. G. Ciarlet
    • 1
  • P. CiarletJr
    • 2
    Email author
  • S. A. Sauter
    • 3
  • C. Simian
    • 4
  1. 1.Department of MathematicsCity University of Hong KongKowloonHong Kong
  2. 2.Laboratoire POEMS, UMR 7231 CNRS/ENSTA/INRIA, ENSTA ParisTech, 828, Boulevard des MaréchauxPalaiseau CedexFrance
  3. 3.Institut für MathematikUniversität ZürichZürichSwitzerland
  4. 4.Department of Computer ScienceUniversity of ChicagoChicagoUSA

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