Fully discrete finite element approaches for time-dependent Maxwell's equations

被引:143
作者
Ciarlet Jr. P. [1 ]
Zou J. [2 ]
机构
[1] Ecl. Natl. Superieure Techniques A., F-75739 Paris Cedex 15, 32, boulevard Victor
[2] Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T.
关键词
Mathematics Subject Classification (1991):65N30, 35L15;
D O I
10.1007/s002110050417
中图分类号
学科分类号
摘要
A fully discrete finite element method is used to approximate the electric field equation derived from time-dependent Maxwell's equations in three dimensional polyhedral domains. Optimal energy-norm error estimates are achieved for general Lipschitz polyhedral domains. Optimal L2-norm error estimates are obtained for convex polyhedral domains.
引用
收藏
页码:193 / 219
页数:26
相关论文
共 22 条
  • [1] Adams R.A., Sobolev Spaces, (1975)
  • [2] Ambrosiano J.J., Brandon S.T., Sonnendrucker E., A finite element formulation of the Darwin PIC model for use on unstructured grids, J. Comput. Physics, 121, pp. 281-297, (1995)
  • [3] Amrouche C., Bernardi C., Dauge M., Girault V., Vector potentials in three-dimensional nonsmooth domains, Math. Meth. Appl. Sci.
  • [4] Assous F., Ciarlet P. Jr., Sonnendrucker E., Resolution of the Maxwell equations in a domain with reentrant corners, RAIRO Math. Modelling Numer. Anal.
  • [5] Assous F., Degond P., Heintze E., Raviart P.-A., Segre J., On a finite-element method for solving the three-dimensional Maxwell equations, J. Comput. Physics, 109, pp. 222-237, (1993)
  • [6] Ciarlet P., Basic error estimates for elliptic problems, Handbook of Numerical Analysis, 2, pp. 17-352, (1991)
  • [7] Ciarlet P. Jr., A decomposition of L<sup>2</sup>(Ω)<sup>3</sup> and an application to magnetostatic equations, Math. Models Meth. App. Sci., 3, pp. 289-301, (1993)
  • [8] Ciarlet P. Jr., Zou J., Finite element convergence for the Darwin model to Maxwell's equations, RAIRO Math. Modelling Numer. Anal., 31, pp. 213-250, (1997)
  • [9] Ciarlet P. Jr., Zou J., Fully Discrete Finite Element Approaches for Time-dependent Maxwell Equations, (1996)
  • [10] Costabel M., A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Math. Meth. Appl. Sci., 12, pp. 365-368, (1990)