Recently, Hofreither, Langer and Pechstein have analyzed a nonstandard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. In the previous work, the primal formulation of the method has been analyzed as an inexact Galerkin scheme, obtaining H 1 error estimates. In this work, we pass to an equivalent mixed formulation. This allows us to derive error estimates in the L 2 -norm, which were so far not available. Many technical tools from our previous analysis remain applicable in this setting.