000124830 001__ 124830
000124830 005__ 20190117191613.0
000124830 0247_ $$2doi$$a10.1137/060674181
000124830 037__ $$aARTICLE 000124830 245__$$aReduced basis error bound computation of parameter-dependent Navier-- Stokes equations by the natural norm approach
000124830 269__ $$a2008 000124830 260__$$c2008
000124830 336__ $$aJournal Articles 000124830 520__$$aThis work focuses on the {\em a posteriori} error estimation for the reduced basis method applied to partial differential equations with quadratic nonlinearity and affine parameter dependence. We rely on natural norms --- {\em local} parameter-dependent norms --- to provide a sharp and computable lower bound of the inf-sup constant. We prove a formulation of the Brezzi--Rappaz--Raviart existence and uniqueness theorem in the presence of two distinct norms. This allows us to relax the existence condition and to sharpen the field variable error bound. We also provide a robust algorithm to compute the Sobolev embedding constants involved in the error bound and in the inf-sup lower bound computation. We apply our method to a steady natural convection problem in a closed cavity, with Grashof number varying from 10 to $10^7$.
000124830 6531_ $$aReduced basis methods 000124830 6531_$$aa posteriori error estimation
000124830 6531_ $$aBrezzi--Rappaz--Raviart theory 000124830 6531_$$asteady incompressible Navier--Stokes equations
000124830 6531_ $$anatural convection 000124830 700__$$0241667$$aDeparis, Simone$$g121157
000124830 773__ $$j46$$k4$$q2039-2067$$tSIAM Journal on Numerical Analysis
000124830 909C0 $$0252102$$pCMCS$$xU10797 000124830 909CO$$ooai:infoscience.tind.io:124830$$pSB$$particle
000124830 937__ $$aCMCS-ARTICLE-2008-019 000124830 973__$$aOTHER$$rREVIEWED$$sPUBLISHED
000124830 980__ aARTICLE