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Article Dans Une Revue Computational & Applied Mathematics Année : 2015

Unification of distance inequalities for linear variational problems

Résumé

In this work a unifying approach is presented that leads to bounds for the distance in natural norms between solutions belonging to different spaces, of well-posed linear variational problems with the same input data. This is done in a general hilbertian framework, and in this sense, well-known inequalities such as Céa 's or Babuška 's for coercive and non coercive problems are extended and/or refined, as mere by-products of this unified setting. More particularly such an approach gives rise to both an improvement and a generalization to the weakly coercive case, of second Strang's inequality for abstract coercive problems. Additionally several aspects specific to linear variational problems are the subject of a thorough analysis beforehand, which also allows for clarifications and further refinements about the concept of weak coercivity.
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Dates et versions

hal-01218082 , version 1 (20-10-2015)

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José Alberto Cuminato, Vitoriano Ruas. Unification of distance inequalities for linear variational problems. Computational & Applied Mathematics, 2015, 34 (3), pp.1009-1033. ⟨10.1007/s40314-014-0163-6⟩. ⟨hal-01218082⟩
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