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Some superconvergence results for mixed finite element methods for linear parabolic problems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1230)

Abstract

We consider continuous-time mixed finite element methods with Raviart-Thomas approximating subspaces for linear parabolic problems. Superconvergence results, L āˆž in time and discrete L 2 in space, are derived for both the solution and gradients (velocity).

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References

  1. Douglas, J. Jr.; Roberts, Jean: Global estimates for mixed methods for second order elliptic equations. To appear in Math. of Comp. 44 (1985).

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  2. Nakata, M.; Weiser, A.; Wheeler, M.F.: Some superconvergence results for mixed finite element methods for elliptic problems on rectangular domains. To appear in MAFELAP Proceedings (1985).

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  3. Raviart, P.A.; Thomas, J.M.: A mixed finite element method for 2nd order elliptic problems in Mathematical Aspects of the Finite Element Method. Lecture Notes in Mathematics, Springer-Verlag, Rome (1975), Heidelberg (1977).

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  4. Weiser, A.; Wheeler, M.F.: On convergence of block-centered finite differences for elliptic problems. To appear.

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  5. Wheeler, M.F.: A priori L 2 estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal. 10, 723–759 (1973).

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Ā© 1986 Springer-Verlag

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Nakata, M., Wheeler, M.F. (1986). Some superconvergence results for mixed finite element methods for linear parabolic problems. In: Hennart, JP. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072679

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  • DOI: https://doi.org/10.1007/BFb0072679

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17200-0

  • Online ISBN: 978-3-540-47379-4

  • eBook Packages: Springer Book Archive