INTERIOR PENALTY PRECONDITIONERS FOR MIXED FINITE-ELEMENT APPROXIMATIONS OF ELLIPTIC PROBLEMS

It is established that an interior penalty method applied to second-or der elliptic problems gives rise to a local operator which is spectral ly equivalent to the corresponding nonlocal operator arising from the mixed finite element method. This relation can be utilized in order to construct preconditioners for the discrete mixed system. As an exampl e, a family of additive Schwarz preconditioners for these systems is c onstructed. Numerical examples which confirm the theoretical results a re also presented.