Superconvergence of mixed finite element semi-discretizations of two time-dependent problems

Jan Brandts

Applications of Mathematics (1999)

  • Volume: 44, Issue: 1, page 43-53
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Brandts, Jan. "Superconvergence of mixed finite element semi-discretizations of two time-dependent problems." Applications of Mathematics 44.1 (1999): 43-53. <http://eudml.org/doc/33026>.

@article{Brandts1999,
abstract = {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.},
author = {Brandts, Jan},
journal = {Applications of Mathematics},
keywords = {superconvergence; diffusion equation; Maxwell equations; mixed elliptic projection; superconvergence; diffusion equation; Maxwell equations; mixed elliptic projection},
language = {eng},
number = {1},
pages = {43-53},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Superconvergence of mixed finite element semi-discretizations of two time-dependent problems},
url = {http://eudml.org/doc/33026},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Brandts, Jan
TI - Superconvergence of mixed finite element semi-discretizations of two time-dependent problems
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 1
SP - 43
EP - 53
AB - 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.
LA - eng
KW - superconvergence; diffusion equation; Maxwell equations; mixed elliptic projection; superconvergence; diffusion equation; Maxwell equations; mixed elliptic projection
UR - http://eudml.org/doc/33026
ER -

References

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  2. Superconvergence for second order triangular mixed and standard finite elements, Report 9 of: Lab. of Sc. Comp, Univ. of Jyväskylä, Finland, 1996. (1996) 
  3. 10.1090/S0025-5718-1985-0771029-9, Math. of Comp. 44(169) (1985), 39–52. (1985) MR0771029DOI10.1090/S0025-5718-1985-0771029-9
  4. Superconvergence for rectangular mixed finite elements, Num. Math. 58 (1990), 2–15. (1990) MR1075159
  5. 10.1137/0913064, SIAM J. Sci. Stat. Comput. 13(5) (1992), 1097–1122. (1992) Zbl0762.65081MR1177800DOI10.1137/0913064
  6. 10.1016/0377-0427(93)90093-Q, J. of Comp. Appl. Math. 47 (1993), 101–121. (1993) Zbl0784.65091MR1226366DOI10.1016/0377-0427(93)90093-Q
  7. A mixed finite element method for second order elliptic problems, Lecture Notes in Mathematics, 606, 1977, pp. 292–315. (1977) MR0483555
  8. Mathematical theory of finite and boundary element methods, A.H. Schatz, V. Thomeé, and W.L. Wendland (eds.), Birkhäuser Verlag, Basel, 1990. (1990) Zbl0701.00028MR1116555

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