| 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:
|
http://hdl.handle.net/10338.dmlcz/134405 |
| . |
| 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 |
| . |
