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Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations

Elżbieta Motyl — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

We consider some abstract nonlinear equations in a separable Hilbert space H and some class of approximate equations on closed linear subspaces of H . The main result concerns stability with respect to the approximation of the space H . We prove that, generically, the set of all solutions of the exact equation is the limit in the sense of the Hausdorff metric over H of the sets of approximate solutions, over some filterbase on the family of all closed linear subspaces of H . The abstract results are...

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