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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 8
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Original Articles

Superconvergence of H1-Galerkin mixed finite element methods for parabolic problems

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Pages 1213-1231 | Received 26 Jul 2009, Accepted 26 Jul 2009, Published online: 21 Sep 2010

References

  • Brezzi , F . 1974 . On the existence, uniqueness, and approximation of saddle-point problems arising from Lagrange multipliers . RAIRO Anal. Numer. , 8 : 129 – 151 .
  • Brezzi , F , Douglas , J and Marini , JLD . 1985 . Two families of mixed finite elements for second order elliptic problems . Numer. Math. , 47 : 217 – 235 .
  • Brezzi , F and Fortin , M . 1991 . Mixed and Hybrid Finite Element Methods , New York : Springer-Verlag .
  • Gunzburger , M . 1989 . Finite Element Methods for Viscous Incompressible Flows , Boston : Academic Press .
  • Johnson , C and Thomée , V . 1981 . Error estimates for some mixed finite element methods for parabolic type problems . R.A.I.R.O. Numer. Anal. , 15 : 41 – 78 .
  • Douglas , J , Dupont , TF and Wheeler , MF . 1975 . H 1 -Galerkin methods for the Laplace and heat equations, in Mathematical Aspects of Finite Elements in Partial Differential Equations , Edited by: de Boor , C . 383 – 415 . New York : Academic Press .
  • Pani , AK . 1998 . An H 1 -Galerkin mixed finite element method for parabolic partial differential equations . SIAM J. Numer. Anal. , 35 ( 2 ) : 712 – 727 .
  • Pani , AK and Fairweather , G . 2002 . H 1 -Galerkin mixed finite element methods for parabolic partial integro-differential equations . IMA J. Numer. Anal. , 22 : 231 – 252 .
  • Pehlivanov , AI , Carey , GF and Lazarov , RD . 1994 . Least square mixed finite elements for second order elliptic problems . SIAM J. Numer. Anal. , 31 ( 5 ) : 1368 – 1377 .
  • Ewing , RE , Lazarov , RD and Wang , J . 1991 . Superconvergence of the velocity along the Gauss lines in mixed finite element methods . SIAM J. Numer. Anal. , 28 ( 4 ) : 1015 – 1029 .
  • Ewing , RE , Liu , M and Wang , J . 2002 . A new superconvergence for the mixed finite element approximations . SIAM J. Numer. Anal. , 40 ( 6 ) : 2133 – 2150 .
  • Douglas , J , Dupont , T and Wheeler , MF . 1978 . A quasi-projection analysis of Galerkin method for parabolic and hyperbolic equations . Math. Comput. , 142 : 345 – 362 .
  • Squeff , MC . 1987 . Superconvergence of mixed finite element methods for parabolic problems . M 2AN Math. Model. Numer. Anal. , 21 : 327 – 352 .
  • Bramble , J and Schatz , AH . 1977 . Higher order local accuracy by averaging in the finite element method . Math. Comput. , 137 : 94 – 111 .
  • Chen , H , Ewing , R and Lazarov , RD . 1998 . Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initia data . Numer. Math. , 78 : 495 – 521 .
  • Durán , R . 1990 . Superconvergence for rectangular mixed finite elements . Numer. Math. , 58 : 287 – 298 .
  • Ewing , RE , Liu , MM and Wang , J . 1999 . Superconvergence of mixed finite element approximations over quadrilaterals . SIAM J. Numer. Anal. , 36 ( 3 ) : 772 – 787 .
  • Adams , RA . 1975 . Sobolev Spaces , New York : Academic Press .
  • Raviart , PA and Thomas , JM . 1977 . A Mixed Finite Element Method for 2nd Order Elliptic Problems, Lecture Notes in Mathematics 606 , 293 – 315 . New York : Springer-Verlag .
  • Cambell , SL , Brenan , KE and Petzold , LR . 1989 . Numerical Solution of Initial Value Problems in Differential-Algebraic Equations , New York : Elsevier .
  • Neittaanmaki , P and Saranen , J . 1981 . A mixed finite element method for the heat flow problem . BIT , 21 : 342 – 346 .

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