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Some nonconforming mixed box schemes for elliptic problems. (English) Zbl 1004.65113

This paper analyzes mathematically three schemes for approximating the Poisson problem posed on 2D triangular meshes. The approximation is based on mixed method with a pair of trial spaces different from the pair of test spaces. It is shown that these schemes are equivalent to a scheme only in \(u\) and to an explicit representation formula for the flux \(p=\nabla u\). This property constitutes a basic ingredient of the numerical analysis of the different schemes. The paper does not include any numerical tests.

MSC:

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