Direct discretization of planar div-curl problems. (English) Zbl 0745.65063

Nicolaides, R. A.

SIAM J. Numer. Anal. 29, No. 1, 32-56 (1992).

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.

Reviewer: I.N.Katz (St.Louis)

MSC:

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

Keywords:

Cauchy-Riemann equations; unstructured mesh techniques; control volume method; div-curl systems; Error estimates