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A new framework for the stability analysis of perturbed saddle-point problems and applications

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 نشر من قبل Qingguo Hong
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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In this paper we prove a new abstract stability result for perturbed saddle-point problems based on a norm fitting technique. We derive the stability condition according to Babuv{s}kas theory from a small inf-sup condition, similar to the famous Ladyzhenskaya-Babuv{s}ka-Brezzi (LBB) condition, and the other standard assumptions in Brezzis theory, in a combined abstract norm. The construction suggests to form the latter from individual {it fitted} norms that are composed from proper seminorms. This abstract framework not only allows for simpler (shorter) proofs of many stability results but also guides the design of parameter-robust norm-equivalent preconditioners. These benefits are demonstrated on mixed variational formulations of generalized Poisson, Stokes, vector Laplace and Biots equations.



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