  For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE
with general coefficients $\mathbf A, \mathbf b,\gamma$ in $L^\infty$ and
symmetric and uniformly positive definite coefficient matrix $\mathbf A$, this
paper proves that mixed finite element problems are uniquely solvable and the
discrete solutions are uniformly bounded, whenever the underlying shape-regular
triangulation is sufficiently fine. This applies to the Raviart-Thomas (RT) and
Brezzi-Douglas-Marini (BDM) finite element families of any order and in any
space dimension and leads to the best-approximation estimate in $H(div)\times
L^2$ as well as in in $L^2\times L^2$ up to oscillations. This generalises
earlier contributions for piecewise Lipschitz continuous coefficients to
$L^\infty$ coefficients. The compactness argument of Schatz and Wang for the
displacement-oriented problem does not apply immediately to the mixed
formulation in $H(div)\times L^2$. But it allows the uniform approximation of
some $L^2$ contributions and can be combined with a recent $L^2$
best-approximation result from the medius analysis. This technique circumvents
any regularity assumption and the application of a Fortin interpolation
operator.
