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On a hierarchical error estimator combined with a stabilized method for the Navier–Stokes equations
Author(s) -
Araya Rodolfo,
Poza Abner H.,
Valentin Frédéric
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20656
Subject(s) - estimator , mathematics , interpolation (computer graphics) , partial differential equation , navier–stokes equations , finite element method , stability (learning theory) , compressibility , mathematical optimization , mathematical analysis , computer science , animation , statistics , physics , computer graphics (images) , machine learning , engineering , thermodynamics , aerospace engineering
Abstract This work combines two complementary strategies for solving the steady incompressible Navier–Stokes model with a zeroth‐order term, namely, a stabilized finite element method and a mesh–refinement approach based on an error estimator. First, equal order interpolation spaces are adopted to approximate both the velocity and the pressure while stability is recovered within the stabilization approach. Also designed to handle advection dominated flows under zeroth‐order term influence, the stabilized method incorporates a new parameter with a threefold asymptotic behavior. Mesh adaptivity driven by a new hierarchical error estimator and built on the stabilized method is the second ingredient. The estimator construction process circumvents the saturation assumption by using an enhancing space strategy which is shown to be equivalent to the error. Several numerical tests validate the methodology. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011