Intrinsic Finite Element Methods for the Computation of Fluxes for Poisson's Equation

Philippe G. Ciarlet (1) , Patrick Ciarlet (2) , Stefan Sauter (3) , C Simian (4)

1 CUHK - City University of Hong Kong [Hong Kong]
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
3 Institut für Mathematik [Zürich]
4 Department of Computer Science, University of Chicago

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.

Mots clés: elliptic boundary value problems; conforming and non-conforming finite element spaces; intrinsic formulation

Domaines: Analyse numérique [math.NA]

Philippe G. Ciarlet, Patrick Ciarlet, Stefan Sauter, C Simian. Intrinsic Finite Element Methods for the Computation of Fluxes for Poisson's Equation. Numerische Mathematik, 2015, pp.30. ⟨10.1007/s00211-015-0730-9⟩. ⟨hal-01160896⟩