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An hp adaptive strategy for finite element approximations of the Navier‐Stokes equations
Author(s) -
Oden J. Tinsley,
Wu Weihan,
Legat Vincent
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650200810
Subject(s) - polygon mesh , finite element method , a priori and a posteriori , computation , mathematical optimization , mathematics , computational fluid dynamics , navier–stokes equations , residual , compressibility , incompressible flow , adaptive strategies , adaptive mesh refinement , flow (mathematics) , algorithm , geometry , computational science , mechanics , physics , history , philosophy , archaeology , epistemology , thermodynamics
Recently, a rigorous a posteriori error estimate, based on the element residual method, for the steady‐state Navier‐Stokes equations has been derived. In this paper, by using this error estimate, we construct an hp adaptive strategy to minimize the total computation costs while achieving a targeted accuracy for steady incompressible viscous flow problems. The basic hp adaptive strategy is to solve the approximate problem in three consecutive stages corresponding to three different meshes, i.e. an initial mesh, an intermediate adaptive h ‐mesh, and a final adaptive hp mesh. Our numerical result shows that the three‐step hp adaptive strategy for the incompressible flow problems indeed provides an accurate approximate solution while keeping the computational costs under control.