Numerical approximation of stiff transmission problems by mixed finite element methods

Abstract.A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element method of Raviart-Thomas is proved to converge with a quasi-optimal error bound.Mathematics Subject Classification. 35J85, 76M30.

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“…when dealing with Tresca condition (8). The duality pairing is defined accordingly to the scalar case.…”

Section: Contact Problemmentioning

confidence: 99%

Mixed formulations for a class of variational inequalities

Slimane

Bendali

Laborde³

2002

Comptes Rendus. Mathématique

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“…but u 1 | ∈ H 1 0 ( ), which contradicts (11). So ( 10) is true and, as α 1 (s 0 ) > 0, we have ∂ s u 1 (s 0 ) = 0 and k = 0.…”

Section: Theoremmentioning

confidence: 87%

“…The measure u m,h is obtained by solving the stiff transmission problem (1) with a mixed finite element method (cf [11]). The following figures present some numerical results.…”

Section: Gradient Of the Discrete Cost Function: Lagragian Formulatio...mentioning

confidence: 99%

Identification of the thickness of a thin layer from boundary measurements

2001

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The aim of this paper is the identification of the thickness of a highly conductive thin layer from boundary measurements. In the introduction, we propose an asymptotic model of the stiff transmission problem. In this context, the thickness of the thin layer appears to be a parameter of the boundary condition of a Ventcel equation. Our goal is to prove the identifiability of this parameter from boundary measurements. After studying the regularity of the direct problem for non-smooth data, identifiability and weak stability results are proved by introducing a suitable admissible parameter space. Numerical experiments are given to illustrate the results.

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