A general mixed covolume framework for constructing conservative schemes for elliptic problems

We present a general framework for the finite volume or covolume schemes de veloped for second order elliptic problems in mixed form, i.e., written as first order systems. We connect these schemes to standard mixed finite elem ent methods via a one-to-one transfer operator between trial and test space s. In the nonsymmetric case (convection-diffusion equation) we show one-hal f order convergence rate for the flux variable which is approximated either by the lowest order Raviart-Thomas space or by its image in the space of d iscontinuous piecewise constants. In the symmetric case (diffusion equation ) a first order convergence rate is obtained for both the state variable (e .g., concentration) and its flux. Numerical experiments are included.