Brandts, Jan H. Superconvergence of mixed finite element semi-discretizations of two time-dependent problems. (English) Zbl 1059.65518 Appl. Math., Praha 44, No. 1, 43-53 (1999). The aim of the paper is to extend some superconvergence results for elliptic problems to time dependent problems. Two-dimensional space variables are discretized by a mixed finite element method whereas time remains continuous. Superconvergence error estimates are derived for a diffusion problem. The author also generalizes P. Monk’s results for lower order finite element approximation of the Maxwell equations to higher order elements. The obtained order of superconvergence for semidiscrete time dependent schemes is the same as for time independent problems. Reviewer: Michal Křížek (Praha) Cited in 14 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory Keywords:superconvergence; diffusion equation; Maxwell equations; mixed elliptic projection × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [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 · doi:10.1007/s002110050064 [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. [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. · Zbl 0624.65109 · doi:10.2307/2007791 [4] R. Durán: Superconvergence for rectangular mixed finite elements. Num. Math. 58 (1990), 2-15. [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 · doi:10.1137/0913064 [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 · doi:10.1016/0377-0427(93)90093-Q [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. [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.