Subgrid stabilization of Galerkin approximations of monotone operators

This paper presents a stabilized Galerkin technique for approximating monot one linear operators in a Hilbert space. The key idea consists in introduci ng an approximation space that is broken up into large scales and small sca les so that the bilinear form associated with the problem satisfies a unifo rm inf-sup condition with respect to this decomposition. An optimal Galerki n approximation is obtained by introducing an artificial diffusion on the s mall scales.