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Direct discretization of planar div-curl problems. (English) Zbl 0745.65063
Author’s summary: A control volume method is proposed for planar div-curl systems. The metod is independent of potential and least squares formulations, and works directly with the div-curl system. The novelty of the technique lies in its use of a single local vector field component and two control volumes rather than the other way round. A discrete vector field theory comes quite naturally from this idea and is developed in the paper. Error estimates are proved for the method, and other ramifications investigated.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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