Abstract
AbstractIn recent works [1, 2], advanced approximation schemes for the numerical calculation of compressible viscous flow were developed, analyzed theoretically and applied successfully to benchmark problems. These methods are based on splitting the Poisson–Stokes system (1.1) describing the motion of a viscous compressible fluid into a generalized Oseen problem for the velocity and a hyperbolic transport equation for the density. Highly refined finite element techniques were proposed for the numerical solution of these separated subproblems of simpler structure; cf. [2]. In this paper, error estimates for a SUPG/(PSPG) and grad‐div stabilized finite element approximation of the generalized Oseen problems that arise in the course of the splitting procedure are presented. LBB‐stable pairs of finite element spaces are used for velocity and pressure. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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