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3D VECTOR POISSON-LIKE PROBLEM WITH A TRIPLET OF INTRINSIC SCALAR BOUNDARY CONDITIONS

Laboratório Nacional de Computação Científica, MCT, Avenida Getúlio Vargas 333, Petrópolis, 25651-070 RJ, Brazil

Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, CNRS-UPR 3251 BP 133 and 91403 Orsay, France

TICAM, The University of Texas at Austin, TX 78712, USA

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ABIMAEL F. D. LOULA

Laboratório Nacional de Computação Científica, MCT, Avenida Getúlio Vargas 333, Petrópolis, 25651-070 RJ, Brazil

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, and

LUIGI QUARTAPELLE

Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20158 Milano, Italy

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https://doi.org/10.1142/S0218202503003094Cited by:2 (Source: Crossref)

Abstract

In this work, we consider the three-dimensional vector Poisson-like equation supplemented by a nonstandard set of three scalar boundary conditions consisting of the simultaneous specification of the divergence of the unknown, its normal component, and the normal component of its curl on the entire boundary. A weak formulation of this elliptic boundary value problem is proposed. Existence and uniqueness of a solution are established under two compatibility conditions. An uncoupled solution algorithm is introduced together with its finite element approximation. The corresponding error analysis is performed.

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