A Modified Finite Volume Approximation of Second-Order Elliptic Equations with Discontinuous Coefficients

A modi ed nite di erence approximation for interface problems in R n is presented The essence of the modi cation falls in the simultaneous discretization of any two normal components of the ux at the opposite faces of the nite volume In this way the continuous normal component of the ux through an interface is approximated by nite di erences with second order consistency The derived scheme has a minimal n point stencil for problems in R Second order convergence with respect to the discrete H norm is proved for a class of interface problems Second order point wise convergence is observed in a series of numerical experiments with D D and D interface problems The numerical experiments presented demonstrate advantages of the new scheme compared with the known schemes which use arithmetic and harmonic averaging of the discontinuous di usion coe cient