Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Global superconvergence
for Maxwell's equations


Authors: Qun Lin and Ningning Yan
Journal: Math. Comp. 69 (2000), 159-176
MSC (1991): Primary 65N30; Secondary 35L15
DOI: https://doi.org/10.1090/S0025-5718-99-01131-X
Published electronically: March 10, 1999
MathSciNet review: 1654029
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the global superconvergence is analysed on two schemes (a mixed finite element scheme and a finite element scheme) for Maxwell's equations in $R^3$. Such a supercovergence analysis is achieved by means of the technique of integral identity (which has been used in the supercovergence analysis for many other equations and schemes) on a rectangular mesh, and then are generalized into more general domains and problems with the variable coefficients. Besides being more direct, our analysis generalizes the results of Monk.


References [Enhancements On Off] (What's this?)

  • 1. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland Publishing Company, 1978. MR 58:25001
  • 2. G. Duvaut, J. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, New York, 1976. MR 58:25191
  • 3. R. Ewing, R. Lazarov, J. Wang, Superconvergence of the velocity along the Gauss lines in mixed finite element methods, SIAM J. Numer. Anal., 28(1991), pp 1015-1029. MR 92e:65149
  • 4. Q. Lin, N. Yan, Superconvergence of mixed finite element methods for Maxwell's equations, Gongcheng Shuxue Xuebao 13(1996), pp 1-10 (in Chinese). MR 98c:65186
  • 5. Q. Lin, N. Yan, The Construction and Analysis of High Efficiency Finite Element Methods, Hebei University Publishers, 1996.
  • 6. Q. Lin, N. Yan, A. Zhou, A rectangle test for interpolated finite elements, Proc. of Sys. Sci. & Sys. Engrg., Great Wall (H. K.) Culture Publish Co., 1991, pp 217-229.
  • 7. P. Monk, A mixed method for approximating Maxwell's equations, SIAM J. Numer. Anal., 28(1991), pp 1610-1634. MR 92j:65173
  • 8. P. Monk, Analysis of a finite element method for Maxwell's equations, SIAM J. Numer. Anal., 29(1992), pp 714-729. MR 93k:65096
  • 9. P. Monk, A comparison of three mixed methods for the time-dependent Maxwell's equations, SIAM J. Sci. Stat. Comput., 13(1992), pp 1097-1122. MR 93j:65184
  • 10. P. Monk, An analysis of Nédélec's method for the special discretization of Maxwell's equations, J. Comput. Appl. Math., 47(1993), pp 101-121. MR 94g:65105
  • 11. P. Monk, Superconvergence of finite element approximations to Maxwell's equations, Numerical Methods for Partial Differential Equations, 10(1994), pp 793-812. MR 95h:65090
  • 12. J. Nédélec, Mixed finite element in R$^3$, Numer. Math., 35(1980), pp 315-341. MR 81k:65125
  • 13. A.H.Schatz, I.H.Sloan, L.B.Wahlbin, Superconvergence in finite element methods and meshes which are locally symmetric with respect to a point, SIAM J. Numer. Anal., 33(1996), pp 505-521. MR 98f:65112
  • 14. L. B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Springer Lecture Notes in Mathematics, 1605, 1995. MR 98j:65083

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (1991): 65N30, 35L15

Retrieve articles in all journals with MSC (1991): 65N30, 35L15


Additional Information

Qun Lin
Affiliation: Institute of Systems Science, Academia Sinica, Beijing, China
Email: glin@bamboo.iss.ac.cn

Ningning Yan
Affiliation: Institute of Systems Science, Academia Sinica, Beijing, China
Email: yan@bamboo.iss.ac.cn

DOI: https://doi.org/10.1090/S0025-5718-99-01131-X
Keywords: Maxwell's equations, superconvergence, finite element
Received by editor(s): September 22, 1997
Received by editor(s) in revised form: March 3, 1998
Published electronically: March 10, 1999
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society