Superconvergence by L2-projection for a stabilized finite volume method for the stationary Navier–Stokes equations

Douglas, 1973, Superconvergence for Galerkin methods for the two-point boundary problem via lacal projections, Numer. Math., 21, 270, 10.1007/BF01436631 Zlamal, 1978, Superconvergence and reduced intergration in the finite element method, Math. Comp., 32, 663, 10.1090/S0025-5718-1978-0495027-4 Wheeler, 1987, Superconvergence recovery of gradient on subdomains from piecewise linear finite element approximations, Numer. Methods Partial Differential Equations, 3, 65, 10.1002/num.1690030106 Douglas, 1989, A superconvergence for mixed finite element methods on rectangular domains, Calcolo, 26, 121, 10.1007/BF02575724 Ewing, 1991, Superconvergence of the velocity along the Gauss lines in mixed finite element methods, SIAM J. Numer. Anal., 28, 1015, 10.1137/0728054 Lin, 1996 Li, 2001, Superconvergence of coupling techniques in combined methods for elliptic equations with singularities, Comput. Math. Appl., 41, 379, 10.1016/S0898-1221(00)00281-9 Li, 2002, Global superconvergence of finite element methods for biharmonic equations and blending surfaces, Comput. Math. Appl., 44, 413, 10.1016/S0898-1221(02)00159-1 Wang, 2004, A superconvergence finite element scheme for the Reissner–Mindlin plate by projection methods, Int. J. Numer. Anal. Model., 1, 99 Liu, 2006, Global superconvergence for optimal control problems governed by Stokes equations, Int. J. Numer. Anal. Model., 3, 283 Brandts, 2006, Superconvergence of least-squares mixed finite elements, Int. J. Numer. Anal. Model., 3, 303 Wang, 2000, A superconvergence analysis for finite element solutions by the least-squares surface fitting on irregular meshes for smooth problems, J. Math. Study, 33, 229 Wang, 2001, Superconvergence of finite element approximations for the Stokes problem by projection methods, SIAM J. Numer. Anal., 39, 1001, 10.1137/S003614290037589X Wang, 2002, Superconvergence analysis for the Navier–Stokes equations, Appl. Numer. Math., 41, 515, 10.1016/S0168-9274(01)00128-3 Li, 2007, Superconvergence of discontinuous Galerkin finite element method for the stationary Navier–Stokes equations, Numer. Methods Partial Differential Equations, 23, 421, 10.1002/num.20188 Li, 2009, Superconvergence by L2-projections for stabilized finite element methods for the Stokes equations, Int. J. Numer. Anal. Model., 6, 711 Ye, 2002, Superconvergence of nonconforming finite element method for the Stokes equations, Numer. Methods Partial Differential Equations, 18, 143, 10.1002/num.1036 Chou, 2007, Superconvergence of finite volume methods for the second order elliptic problem, Comput. Methods Appl. Mech. Engrg., 196, 3706, 10.1016/j.cma.2006.10.025 Cui, 2009, Superconvergence of finite volume methods for the Stokes equations, Numer. Methods Partial Differential Equations, 25, 1212, 10.1002/num.20399 Cai, 1991, The finite volume element method for diffusion equations on general triangulations, SIAM J. Numer. Anal., 28, 392, 10.1137/0728022 Chen, 2006, The control volume finite element methods and their applications to multiphase flow, Netw. Heterog. Media, 1, 689, 10.3934/nhm.2006.1.689 Chou, 1999, Error estimates in L2,H1 and L∞ in co-volume methods for elliptic and parabolic problems: a unified approach, Math. Comp., 69, 103, 10.1090/S0025-5718-99-01192-8 Li, 1987, Generalized difference methods for a nonlinear Dirichlet problem, SIAM J. Numer. Anal., 24, 77, 10.1137/0724007 Bochev, 2006, Stabilization of low-order mixed finite elements for the Stokes equations, SIAM J. Numer. Anal., 44, 82, 10.1137/S0036142905444482 Li, 2007, A new stabilized finite element method for the transient Navier–Stokes equations, Comput. Methods Appl. Mech. Eng., 197, 22, 10.1016/j.cma.2007.06.029 Li, 2008, A stabilized finite element method based on two local gauss integrations for the Stokes equations, J. Comput. Appl. Math., 214, 58, 10.1016/j.cam.2007.02.015 Heywood, 1982, Finite-element approximations of the nonstationary Navier–Stokes problem. Part I: Regularity of solutions and second-order spatial discretization, SIAM J. Numer. Anal., 19, 275, 10.1137/0719018 Kellogg, 1976, A regularity result for the Stokes problem in a convex polygon, J. Funct. Anal., 21, 397, 10.1016/0022-1236(76)90035-5 Adams, 1975 Li, 2010, Convergence and stability of a stabilized finite volume method for the stationary Navier–Stokes equations, BIT, 50, 823, 10.1007/s10543-010-0277-1 He, 2008, A simplified two-level method for the steady Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., 197, 1568, 10.1016/j.cma.2007.11.032 Li, 2009, A new stabilized finite volume method for the stationary Stokes equations, Adv. Comput. Math., 30, 141, 10.1007/s10444-007-9060-5 Ciarlet, 1978 Ye, 2001, On the relationship between finite volume and finite element methods applied to the Stokes equations, Numer. Methods Partial Differential Equations, 5, 440, 10.1002/num.1021