Subgrid stabilization of Galerkin approximations of linear monotone operators

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Abstract
This paper presents a stabilized Galerkin technique for approximating monotone linear operators in a Hilbert space. The key idea consists in introducing an approximation space that is broken up into resolved scales and subgrid scales so that the bilinear form associated with the problem satisfies a uniform inf‐sup condition with respect to this decomposition. An optimal Galerkin approximation is obtained by introducing an artificial diffusion on the subgrid scales.

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