On the p- and hp-extension of Nédélec's curl-conforming elements

Journal of Computational and Applied Mathematics - Tập 53 - Trang 117-137 - 1994
Peter Monk1
1Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, United States

Tài liệu tham khảo

Babuška, 1990, The p- and h-p versions of the finite element method, an overview, Comput. Methods Appl. Mech. Engrg, 80, 5, 10.1016/0045-7825(90)90011-A Barton, 1987, New vector finite elements for three-dimensional magnetic computation, J. Appl. Phys., 61, 3919, 10.1063/1.338584 Bossavit, 1988, A rationale for “edge elements” in 3-D fields computations, IEEE Trans. Mag., 24, 74, 10.1109/20.43860 Bossavit, 1990, Solving Maxwell equations in a closed cavity, and the question of ‘spurious’ modes, IEEE Trans. Mag., 25, 702, 10.1109/20.106414 Bossavit, 1983, The “TRIFOU” code: Solving the 3-D eddy-currents problem by using h as the state variable, IEEE Trans. Mag., 19, 2465, 10.1109/TMAG.1983.1062817 Brezzi, 1974, On the existence and uniqueness of saddle-point problems arising from Lagrange multipliers, RAIRO Anal. Numér., 8, 129 Ciarlet, 1978, The Finite Element Method for Elliptic Problems, 4 Girault, 1986 G. Hsiao and C. Schwab, Discretization of the Poincaré-Steklov operator in combined finite and boundary element methods, Preprint. Kanayama, 1990, Three-dimensional magnetostatic analysis using Nédélec's elements, IEEE Trans. Mag., 26, 682, 10.1109/20.106409 Křížek, 1989, On time-harmonic Maxwell equations with nonhomogeneous conductivities: solvability and FE-approximation, Apl. Mat., 34, 480, 10.21136/AM.1989.104379 Levillain, 1992, Eigenvalue approximation by mixed methods for resonant inhomogeneous cavities with metallic boundaries, Math. Comp., 58, 11, 10.1090/S0025-5718-1992-1106975-3 F. Milner and M. Suri, Mixed finite element methods for quasilinear second order elliptic problems: the p version, Preprint. Monk, 1991, A mixed method for approximating Maxwell's equations, SIAM J. Numer. Anal., 28, 1610, 10.1137/0728081 Monk, 1992, A finite element method for approximating the time-harmonic Maxwell equations, Numer. Math., 63, 243, 10.1007/BF01385860 Nédélec, 1980, Mixed finite elements in R3, Numer. Math., 35, 315, 10.1007/BF01396415 Nédélec, 1982, Éléments finis mixtes incompressibles pour l'équation de Stokes dans R3, Numer. Math., 39, 97, 10.1007/BF01399314 Suri, 1990, On the stability and convergence of higher-order mixed finite element methods for second-order elliptic problems, Math. Comp., 54, 1, 10.1090/S0025-5718-1990-0990603-X