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Augmented spaces, two-level methods, and stabilizing subgrids. (English) Zbl 1021.76024

Summary: Starting from the already known relationship between stabilized methods, augmented spaces and residual-free bubbles (RFB), the paper introduces a possible way of mimicking the effect of RFB just by constructing a suitable subgrid and then solving the standard Galerkin equations on the modified grid. Concentrating on the model problem of linear convection-dominated equations, we give sufficient conditions on the subgrid that ensure stability, and error bounds for the same type of standard stabilizing procedures.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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