Computer Methods in Applied Mechanics and Engineering
A posteriori error estimation of steady-state finite element solutions of the Navier—Stokes equations by a subdomain residual method
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Cited by (22)
A review of VMS a posteriori error estimation with emphasis in fluid mechanics
2023, Computer Methods in Applied Mechanics and EngineeringA posteriori error estimations for mixed finite element approximations to the Navier–Stokes equations based on Newton-type linearization
2020, Journal of Computational and Applied MathematicsVariational multiscale a posteriori error estimation for systems. Application to linear elasticity
2015, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :Typically, these differential equations are applied to a subdomain (an element or a patch of elements). Many researchers have worked on this matter [6–17]. Recently, Ainsworth et al. have worked on error bounds for elasticity and transport equation in 3D [18,19].
Variational multiscale a posteriori error estimation for systems: The Euler and Navier-Stokes equations
2015, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :The element residual method is applied to estimate the error of the incompressible Navier–Stokes equations by [15–17] and to symmetrizable systems and the compressible Navier–Stokes equations by [18,19]. The subdomain residual method proposed in [20] estimates the error of the incompressible Navier–Stokes equations, where local primal problems are solved in patches of elements. Recently, based on the variational multiscale theory, various papers propose to compute explicitly the subgrid scales (or error) on patches of elements [21,22] or inside each element with an enriched basis [23].
A new parallel finite element algorithm for the stationary Navier-Stokes equations
2011, Finite Elements in Analysis and DesignCitation Excerpt :This is, in a way, related to the residual-type methods for a posteriori error estimation in finite element analysis (cf. [50–52]). We refer, for example, to [53–55] for such residual-type a posteriori error estimations for the steady Navier–Stokes equations, and to [56–59] for the unsteady Navier–Stokes equations. However, the main philosophy behind our present paper is that we should treat phenomena of different scales by different tools [11], which is different from that of a posteriori error estimation.
A posteriori error estimations for mixed finite-element approximations to the NavierStokes equations
2011, Journal of Computational and Applied Mathematics