References
- Ainsworth , M and Oden , JT . 1997 . A posteriori error estimation in finite element analysis . Comput. Methods Appl. Mech. Eng. , 142 : 1 – 88 .
- Bank , RB and Weiser , A . 1985 . Some a posteriori error estimators for elliptic partial differential equations . Math. Comput. , 44 : 283 – 301 .
- Eriksson , K and Johnson , C . 1991 . Adaptive finite element methods for parabolic problems: I. A linear model problem . SIAM J. Numer. Anal. , 28 : 43 – 77 .
- Eriksson , K , Johnson , C and Thomée , V . 1985 . Time discretization of parabolic problems by the discontinuous Galerkin method . RAIRO Modél. Math. Anal. Numér. , 19 : 611 – 643 .
- Meidner , D and Vexler , B . 2008 . A priori error estimates for space-time finite element discretization of parabolic optimal control problems, Part I: Problems without control constraints . SIAM J. Control Optim. , 47 ( 3 ) : 1150 – 1177 .
- Meidner , D and Vexler , B . 2008 . A priori error estimates for space-time finite element discretization of parabolic optimal control problems, Part I: Problems with control constraints . SIAM J. Control Optim. , 47 ( 3 ) : 1301 – 1329 .
- Cascön , JM , Ferragut , L and Asensio , MI . 2006 . Space-time adaptive algorithm for the mixed parabolic problem . Numer. Math. , 103 : 367 – 392 .
- Larson , MG and Malqvist , A . 2011 . A posteriori error estimates for mixed finite element approximations of parabolic problems . Numer. Math. , 118 : 33 – 48 .
- Memon , S , Nataraj , N and Pani , AK . 2012 . An a posteriori error analysis of mixed finite element Galerkin approximations to second-order linear parabolic problems . SIAM J. Numer. Anal. , 50 : 1367 – 1393 .
- Makridakis , C and Nochetto , RH . 2003 . Elliptic reconstruction and a posteriori error estimates for parabolic problems . SIAM J. Numer. Anal. , 41 : 1585 – 1594 .
- Hou , T . Mixed DG finite element methods for linear parabolic equations , (submitted)
- Lions , J and Magenes , E . 1972 . Non homogeneous boundary value problems and applications, Grandlehre B. 181 , New York : Springer-Verlag .
- Douglas , J and Roberts , JE . 1985 . Global estimates for mixed finite element methods for second-order elliptic equations . Math. Comput. , 44 : 39 – 52 .
- Raviart , PA and Thomas , JM . 1977 . “ A Mixed Finite Element Method for 2nd Order Elliptic Problems, Mathematical Aspects of the Finite Element Method ” . In Lecture Notes in Mathematics , Vol. 606 , 292 – 315 . Berlin : Springer .
- Brezzi , F and Fortin , M . 1991 . Mixed and hybrid finite element methods , Vol. 95 , 65 – 187 . New York : Springer-Verlag .
- Houston , P and Süli , E . 1997 . A posteriori error analysis for linear convection-diffusion problems under weak mesh regularity assumptions , Oxford , , UK : Report 97/03, Oxford University Computing Laboratory .