The Mathematics of Finite Elements and Applications II MAFELAP1975

Abstract : This paper describes theory and methods for developing a posteriori error estimates and an adaptive strategy for hp-finite element approximations of the incompressible Navier-Stokes equations. For an error estimation, use is made of a new approach which is based on the work of Ainsworth, Wu and the author. That theory has been shown to produce good results for general elliptic systems and general hp-finite element method% Recently, these techniques have been extended to the Navier-Stokes equations A three-step adaptive algorithm is also described which produces reasonable hp meshes very efficiently. These techniques are applied to representative transient and steady state problems of incompressible viscous flow.