The numerical solution of Dirichlet’s problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first- and zero-order terms is considered. The mixed finite element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in \(L^2\) are demonstrated for the relevant functions. Error estimates are also derived in \(L^q\), \(2\leq q\leq + \infty\).