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SUMMARY:Guaranteed and robust a posteriori error estimates and stopping cr
 iteria for iterative linearizations and linear solvers
DTSTART:20101201T161500
DTSTAMP:20260509T211758Z
UID:774301f7873e28aad9ed9777996a98d89d9766db7266556931472306
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Martin Vohralík\nWe present the a posteriori error estimat
 es of [1] and [2] which enable to take into account the linearization erro
 r in approximation of nonlinear problems and the algebraic error in the so
 lution of linear systems associated to the given numerical discretization.
  Our estimates allow to distinguish\, estimate separately\, and compare th
 ese different error sources. Consequently\, the iterative (Newton\, quasi-
 Newton) linearization or iterative solution of linear algebraic systems ca
 n be stopped whenever the individual errors drop to the level at which the
 y do not affect significantly the overall error. This can lead to importan
 t computational savings\, as performing an excessive number of unnecessary
  linearization/linear solver iterations can be avoided. Moreover\, due to 
 their local efficiency\, our estimators also allow to accurately predict t
 he error spatial distribution and thus they are suitable for local adaptiv
 e mesh refinement. Finally\, they give a fully computable upper bound on t
 he overall error. This allows to devise an adaptive strategy enabling to a
 chieve a user-given precision at minimal cost. Numerical experiments illus
 trate the theoretical developments.
LOCATION:MAA110
STATUS:CONFIRMED
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