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Fictitious domains, $$\text{H(div)}$$ finite elements and Neumann condition: The inf-sup condition. (Domaines fictifs, éléments finis $$\text{H(div)}$$ et condition de Neumann: Le problème de la condition inf-sup.) (French. Abridged English version) Zbl 0931.65112
Summary: Approximation of the Neumann problem for a second-order elliptic operator by a fictitious domain method with a Lagrange multiplier on the boundary is considered. The problem is written in its vectorial dual formulation and H(div) mixed finite elements for the vector unknown and H$$^{{1\over 2}}$$ conforming elements for the multiplier are used. The uniform inf-sup condition is demonstrated under a compatibility condition between surface and volume meshes.

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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