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IMA Journal of Numerical Analysis 2001 21(1):165-197; doi:10.1093/imanum/21.1.165
© 2001 by Institute of Mathematics and its Applications
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Subgrid stabilization of Galerkin approximations of linear monotone operators

J.-L. Guermond1

1 LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France, e-mail: guermond{at}limsi.fr

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.

Key Words: linear first-order PDEs, non-coercive linear operator, monotone operators, hierarchical finite elements, stabilization, subgrid modelling, artificial viscosity

Received 16 September 1998. Accepted 17 January 2000.


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