Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations

Verfürth, 1989, A posteriori error estimators for the Stokes equations, Numer. Math., 55, 309, 10.1007/BF01390056 Verfürth, 1991, A posteriori error estimators for the Stokes equations II non-conforming discretizations, Numer. Math., 60, 235, 10.1007/BF01385723 Dari, 1995, Error estimators for nonconforming finite element approximations of the Stokes problem, Math. Comp., 64, 1017, 10.1090/S0025-5718-1995-1284666-9 Ladevèze, 1983, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal., 20, 485, 10.1137/0720033 Luce, 2004, A local a posteriori error estimator based on equilibrated fluxes, SIAM J. Numer. Anal., 42, 1394, 10.1137/S0036142903433790 Ainsworth, 2007, A posteriori error estimation for discontinuous Galerkin finite element approximation, SIAM J. Numer. Anal., 45, 1777, 10.1137/060665993 Ern, 2007, An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems, C. R. Acad. Sci. Paris Ser., 345, 709, 10.1016/j.crma.2007.10.036 Hannukainen, 2012, A unified framework for a posteriori error estimation for the Stokes problem, Numer. Math., 122, 725, 10.1007/s00211-012-0472-x Kim, 2014, Fully computable a posteriori error estimates for the Stokes equation without the global inf-sup constant, Comput. Math. Appl., 67, 681, 10.1016/j.camwa.2013.12.011 Bringmann, 2016, Guaranteed velocity error control for the pseudostress approximation of the Stokes equations, Numer. Methods Partial Differential Equations, 32, 1411, 10.1002/num.22056 Kim, 2013, A staggered discontinuous Galerkin method for the Stokes system, SIAM J. Numer. Anal., 51, 3327, 10.1137/120896037 Chung, 2017, An adaptive SDG method for the Stokes system, J. Sci. Comput., 70, 766, 10.1007/s10915-016-0265-y Kim, 2012, Flux reconstruction for the P2 nonconforming finite element method with application to a posteriori error estimation, Appl. Numer. Math., 62, 1701, 10.1016/j.apnum.2012.06.027 Chung, 2017, Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method, J. Sci. Comput. Karakashian, 2003, A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems, SIAM J. Numer. Anal., 41, 2374, 10.1137/S0036142902405217 Achdou, 2003, A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations, Numer. Math., 96, 17, 10.1007/s00211-002-0436-7 Ainsworth, 2010, A framework for obtaining guaranteed error bounds for finite element approximations, J. Comput. Appl. Math., 234, 2618, 10.1016/j.cam.2010.01.037 Horgan, 1983, On inequalities of Korn, Friedrichs and Babus̆ka-Aziz, Arch. Ration. Mech. Anal., 82, 165, 10.1007/BF00250935 Stoyan, 1999, Towards discrete Velte decompositions and narrow bounds for inf-sup constants, Comput. Math. Appl., 38, 243, 10.1016/S0898-1221(99)00254-0 Carstensen, 2011, A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the Stokes problem, SIAM J. Numer. Anal., 49, 2501, 10.1137/100816237 Arnold, 1985, Mixed and nonconforming finite element methods: imlementation, postprocessing and error estimates, RAIRO Modél. Math. Anal. Numér., 19, 7, 10.1051/m2an/1985190100071 Arbogast, 1995, On the implementation of mixed methods as nonconforming methods for second-order elliptic problems, Math. Comp., 64, 943 Vohralík, 2010, Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods, Math. Comp., 79, 2001, 10.1090/S0025-5718-2010-02375-0 Houston, 2009, A mixed DG methods for linearized incompressible magnetohydrodynamics, J. Sci. Comput., 40, 281, 10.1007/s10915-008-9265-x Bank, 1991, A posteriori error estimates for the Stokes problem, SIAM J. Numer. Anal., 28, 591, 10.1137/0728033