MIXED COVOLUME METHODS FOR ELLIPTIC PROBLEMS ON TRIANGULAR GRIDS

We consider a covolume or finite volume method for a system of first-o rder PDEs resulting from the mixed formulation of the variable coeffic ient-matrix Poisson equation with the Neumann boundary condition. The system may represent either the Darcy law and the mass conservation la w in anisotropic porous media flow, or Fourier law and energy conserva tion. The velocity and pressure are approximated by the lowest order R aviart-Thomas space on triangles. We prove its first-order optimal rat e of convergence for the approximate velocities in the L-2 -and H(div; Omega)-norms as well as for the approximate pressures in the L-2-norm . Numerical experiments are included.