A priori and a posteriori analysis of finite volume discretizations of Darcy?s equations, Numerische Mathematik, vol.96, issue.1, pp.17-42, 2003. ,
DOI : 10.1007/s00211-002-0436-7
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods, Recent advances in adaptive computation, pp.1-14, 2005. ,
DOI : 10.1090/conm/383/07154
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation, SIAM Journal on Numerical Analysis, vol.45, issue.4, pp.1777-1798, 2007. ,
DOI : 10.1137/060665993
A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, 2000. ,
DOI : 10.1016/S0045-7825(96)01107-3
On the implementation of mixed methods as nonconforming methods for second-order elliptic problems, Math. Comp, vol.64, pp.211-943, 1995. ,
Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates, ESAIM: Mathematical Modelling and Numerical Analysis, vol.19, issue.1, pp.7-32, 1985. ,
DOI : 10.1051/m2an/1985190100071
A stable finite element for the stokes equations, Calcolo, vol.21, issue.4, pp.337-344, 1984. ,
DOI : 10.1007/BF02576171
Some Error Estimates for the Box Method, SIAM Journal on Numerical Analysis, vol.24, issue.4, pp.777-787, 1987. ,
DOI : 10.1137/0724050
A Note on the Poincar?? Inequality for Convex Domains, Zeitschrift f??r Analysis und ihre Anwendungen, vol.22, issue.4, pp.751-756, 2003. ,
DOI : 10.4171/ZAA/1170
A dG method for the Stokes equations related to nonconforming approximations. HAL preprint 00380772, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00380772
Mimetic finite difference method for the Stokes problem on polygonal meshes, Journal of Computational Physics, vol.228, issue.19, pp.19-7215, 2009. ,
DOI : 10.1016/j.jcp.2009.06.034
Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numerische Mathematik, vol.65, issue.2, pp.211-224, 1979. ,
DOI : 10.1007/BF01399555
Equilibrated residual error estimates are p-robust, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.13-14, pp.13-14, 2009. ,
DOI : 10.1016/j.cma.2008.12.010
Equilibrated residual error estimator for edge elements, Mathematics of Computation, vol.77, issue.262, pp.651-672, 2008. ,
DOI : 10.1090/S0025-5718-07-02080-7
Stabilized mixed methods for the Stokes problem, Numerische Mathematik, vol.36, issue.1-2, pp.1-2, 1988. ,
DOI : 10.1007/BF01395886
Stability of Higher-Order Hood???Taylor Methods, SIAM Journal on Numerical Analysis, vol.28, issue.3, pp.3-581, 1991. ,
DOI : 10.1137/0728032
Mixed and hybrid finite element methods, 1991. ,
DOI : 10.1007/978-1-4612-3172-1
On the Stabilization of Finite Element Approximations of the Stokes Equations, Efficient solutions of elliptic systems of Notes Numer. Fluid Mech. Vieweg, pp.11-19, 1984. ,
DOI : 10.1007/978-3-663-14169-3_2
Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations, Mathematics of Computation, vol.76, issue.259, pp.259-1119, 2007. ,
DOI : 10.1090/S0025-5718-07-01951-5
A unifying theory of a posteriori finite element error control, Numerische Mathematik, vol.55, issue.4, pp.617-637, 2005. ,
DOI : 10.1007/s00211-004-0577-y
Arnold-Winther mixed finite elements for the Stokes problem, Submitted to SIAM J. Sci. Comput, 2010. ,
A unifying theory of a posteriori error control for discontinuous Galerkin FEM, Numerische Mathematik, vol.75, issue.23, pp.363-379, 2009. ,
DOI : 10.1007/s00211-009-0223-9
A unifying theory of a posteriori error control for nonconforming finite element methods, Numerische Mathematik, vol.34, issue.3, pp.473-502, 2007. ,
DOI : 10.1007/s00211-007-0068-z
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems, M2AN Math. Model. Numer. Anal, vol.43, pp.5-867, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00271527
Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, Revue fran??aise d'automatique informatique recherche op??rationnelle. Math??matique, vol.7, issue.R3, pp.3-33, 1973. ,
DOI : 10.1051/m2an/197307R300331
Error estimators for nonconforming finite element approximations of the Stokes problem, Mathematics of Computation, vol.64, issue.211, pp.211-1017, 1995. ,
DOI : 10.1090/S0025-5718-1995-1284666-9
Explicit error bounds in a conforming finite element method, Mathematics of Computation, vol.68, issue.228, pp.1379-1396, 1999. ,
DOI : 10.1090/S0025-5718-99-01093-5
On the LBB condition in the numerical analysis of the Stokes equations, Applied Numerical Mathematics, vol.54, issue.3-4, pp.3-4, 2005. ,
DOI : 10.1016/j.apnum.2004.09.005
Reliable a posteriori error control for nonconformal finite element approximation of Stokes flow, Math. Comp, vol.74, pp.252-1599, 2005. ,
Study of the mixed finite volume method for Stokes and Navier-Stokes equations, Numerical Methods for Partial Differential Equations, vol.7, issue.1, pp.137-171, 2009. ,
DOI : 10.1002/num.20333
URL : https://hal.archives-ouvertes.fr/hal-00110911
An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems, C. R. Math. Acad. Sci. Paris, vol.345, pp.12-709, 2007. ,
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection???diffusion???reaction problems, Journal of Computational and Applied Mathematics, vol.234, issue.1, pp.114-130, 2010. ,
DOI : 10.1016/j.cam.2009.12.009
URL : https://hal.archives-ouvertes.fr/hal-00193540
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids, Comptes Rendus Mathematique, vol.347, issue.7-8, pp.7-8, 2009. ,
DOI : 10.1016/j.crma.2009.01.017
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.198-223, 2010. ,
DOI : 10.1137/090759008
URL : https://hal.archives-ouvertes.fr/hal-00383692
Stabilized finite element methods In Incompressible computational fluid dynamics: trends and advances, pp.87-107, 1993. ,
Error Analysis of Galerkin Least Squares Methods for the Elasticity Equations, SIAM Journal on Numerical Analysis, vol.28, issue.6, pp.6-1680, 1991. ,
DOI : 10.1137/0728084
URL : https://hal.archives-ouvertes.fr/inria-00075505
Finite element methods for Navier-Stokes equations Theory and algorithms, of Springer Series in Computational Mathematics, 1986. ,
On numerical methods for the Stokes problem In Energy methods in finite element analysis, pp.243-264, 1979. ,
Solution of variational inequalities in mechanics, of Applied Mathematical Sciences, 1988. ,
DOI : 10.1007/978-1-4612-1048-1
Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem, J. Sci. Comput, vol.2223, pp.347-370, 2005. ,
A new finite element formulation for computational fluid dynamics: V. Circumventing the babu??ka-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering, vol.59, issue.1, pp.1-85, 1986. ,
DOI : 10.1016/0045-7825(86)90025-3
A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems, SIAM Journal on Numerical Analysis, vol.41, issue.6, pp.2374-2399, 2003. ,
DOI : 10.1137/S0036142902405217
A posteriori error analysis for locally conservative mixed methods, Mathematics of Computation, vol.76, issue.257, pp.43-66, 2007. ,
DOI : 10.1090/S0025-5718-06-01903-X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2285
Error Estimate Procedure in the Finite Element Method and Applications, SIAM Journal on Numerical Analysis, vol.20, issue.3, pp.3-485, 1983. ,
DOI : 10.1137/0720033
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes, SIAM Journal on Numerical Analysis, vol.42, issue.4, pp.1394-1414, 2004. ,
DOI : 10.1137/S0036142903433790
URL : https://hal.archives-ouvertes.fr/inria-00343040
An optimal Poincar?? inequality for convex domains, Archive for Rational Mechanics and Analysis, vol.5, issue.1, pp.286-292, 1960. ,
DOI : 10.1007/BF00252910
Finite element methods for fluids, 1989. ,
Approximations in elasticity based on the concept of function space, Quarterly of Applied Mathematics, vol.5, issue.3, pp.241-269, 1947. ,
DOI : 10.1090/qam/25902
A posteriori error estimation for nonlinear variational problems by duality theory, Journal of Mathematical Sciences, vol.24, issue.1, pp.28-201, 1997. ,
DOI : 10.1007/BF02673600
A posteriori error estimates for the generalized Stokes problem, Journal of Mathematical Sciences, vol.8, issue.R-2, pp.1828-1843, 2007. ,
DOI : 10.1007/s10958-007-0092-7
Conforming finite element methods for incompressible and nearly incompressible continua In Large-scale computations in fluid mechanics, Lectures in Appl. Math. Amer. Math. Soc, vol.22, issue.2, pp.221-244, 1983. ,
Some new families of finite elements for the stokes equations, Numerische Mathematik, vol.18, issue.8, pp.827-838, 1990. ,
DOI : 10.1007/BF01405291
URL : https://hal.archives-ouvertes.fr/inria-00075604
A numerical solution of the Navier-Stokes equations using the finite element technique, Computers & Fluids, vol.1, issue.1, pp.1-73, 1973. ,
DOI : 10.1016/0045-7930(73)90027-3
A combined conjugate gradient - multi-grid algorithm for the numerical solution of the Stokes problem, IMA Journal of Numerical Analysis, vol.4, issue.4, pp.441-455, 1984. ,
DOI : 10.1093/imanum/4.4.441
A posteriori error estimators for the Stokes equations, Numerische Mathematik, vol.4, issue.3, pp.309-325, 1989. ,
DOI : 10.1007/BF01390056
A posteriori error estimators for the Stokes equations II non-conforming discretizations, Numerische Mathematik, vol.55, issue.1, pp.235-249, 1991. ,
DOI : 10.1007/BF01385723
A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations, SIAM Journal on Numerical Analysis, vol.45, issue.4, pp.1570-1599, 2007. ,
DOI : 10.1137/060653184
A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization, Comptes Rendus Mathematique, vol.346, issue.11-12, pp.11-12, 2008. ,
DOI : 10.1016/j.crma.2008.03.006
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods, Numerische Mathematik, vol.59, issue.3, pp.121-158, 2008. ,
DOI : 10.1007/s00211-008-0168-4
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods, Mathematics of Computation, vol.79, issue.272, pp.272-2001, 2010. ,
DOI : 10.1090/S0025-5718-2010-02375-0
Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients, Journal of Scientific Computing, vol.24, issue.2, pp.397-438, 2011. ,
DOI : 10.1007/s10915-010-9410-1
A unified posteriori error estimator for finite element methods for the Stokes equations, 2010. ,