Previous |  Up |  Next


Title: Superconvergence of mixed finite element semi-discretizations of two time-dependent problems (English)
Author: Brandts, Jan H.
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 44
Issue: 1
Year: 1999
Pages: 43-53
Summary lang: English
Category: math
Summary: We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation for the error in the space discretization can be performed in the same way as for the underlying elliptic problem. (English)
Keyword: superconvergence
Keyword: diffusion equation
Keyword: Maxwell equations
Keyword: mixed elliptic projection
MSC: 65M60
MSC: 65N30
MSC: 78M10
idZBL: Zbl 1059.65518
idMR: MR1666846
DOI: 10.1023/A:1022220219953
Date available: 2009-09-22T17:59:57Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] J.H. Brandts: Superconvergence and a posteriori error estimation for triangular mixed finite elements.Num. Math. 68(3) (1994), 311–324. Zbl 0823.65103, MR 1313147, 10.1007/s002110050064
Reference: [2] J.H. Brandts: Superconvergence for second order triangular mixed and standard finite elements.Report 9 of: Lab. of Sc. Comp, Univ. of Jyväskylä, Finland, 1996.
Reference: [3] J. Douglas and J.E. Roberts: Global estimates for mixed methods for second order elliptic problems.Math. of Comp. 44(169) (1985), 39–52. MR 0771029, 10.1090/S0025-5718-1985-0771029-9
Reference: [4] R. Durán: Superconvergence for rectangular mixed finite elements.Num. Math. 58 (1990), 2–15. MR 1075159
Reference: [5] P. Monk: A comparison of three mixed methods for the time-dependent Maxwell’s equations.SIAM J. Sci. Stat. Comput. 13(5) (1992), 1097–1122. Zbl 0762.65081, MR 1177800, 10.1137/0913064
Reference: [6] P. Monk: An analysis of Nédélec’s method for the spatial discretization of Maxwell’s equations.J. of Comp. Appl. Math. 47 (1993), 101–121. Zbl 0784.65091, MR 1226366, 10.1016/0377-0427(93)90093-Q
Reference: [7] P.A. Raviart and J.M. Thomas: A mixed finite element method for second order elliptic problems.Lecture Notes in Mathematics, 606, 1977, pp. 292–315. MR 0483555
Reference: [8] : Mathematical theory of finite and boundary element methods.A.H. Schatz, V. Thomeé, and W.L. Wendland (eds.), Birkhäuser Verlag, Basel, 1990. Zbl 0701.00028, MR 1116555


Files Size Format View
AplMat_44-1999-1_4.pdf 333.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo