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On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions. (English) Zbl 0949.65116
This paper considers the two-dimensional vector Poisson equation with two boundary conditions imposing given values to the normal component and to the divergence; these conditions are not natural with respect to the usual variational formulations. The kernels of the associated and transposed operators are studied and the variational formulation is modified and reformulated in a well-posed manner. Then, a splitting method leads to an uncoupled numerical algorithm requiring to solve only scalar Poisson equations and an auxiliary problem for a scalar boundary unknown. Finally, the problem is approximated by finite element methods, corresponding error estimates are obtained and a few numerical tests illustrate the pertinency of the method.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N15 Error bounds for boundary value problems involving PDEs
35J50 Variational methods for elliptic systems
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