A mixed–FEM and BEM coupling for a three-dimensional eddy current problem

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1. [1] A. Alonso and A. Valli, An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations, Math. Comp. 68 (1999) 607–631. Zbl1043.78554
2. [2] H. Ammari, A. Buffa and J.-C. Nédélec, A justification of eddy currents model for the Maxwell equations. SIAM J. Appl. Math. 60 (2000) 1805–1823. Zbl0978.35070
3. [3] C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional nonsmooth domains. Math. Methods Appl. Sci. 21 (1998) 823–864. Zbl0914.35094
4. [4] A. Bermúdez, R. Rodríguez and P. Salgado, A finite element method with Lagrange multipliers for low-frequency harmonic Maxell equations. SIAM J. Numer. Anal. 40 (2002) 1823–1849. Zbl1033.78009
5. [5] A. Bossavit and J. Vérité, The TRIFOU code: Solving the 3-D eddy–currents problem by using H as state variable. IEEE Trans. Mag. 19 (1983) 2465–2470. 
6. [6] A. Bossavit, Two dual formulations of the 3-D eddy-currents problem. COMPEL 4 (1985) 103–116. 
7. [7] A. Bossavit, A rationale for edge elements in 3-D field computations. IEEE Trans. Mag. 24 (1988) 74–79. 
8. [8] A. Bossavit, The computation of eddy-currents in dimension 3 by using mixed finite elements and boundary elements in association. Math. Comput. Modelling 15 (1991) 33–42. Zbl0725.65112
9. [9] A. Bossavit, Électromagnétisme, en vue de la modélisation. Springer-Verlag, Paris, Berlin, Heidelberg (1993). Zbl0787.65090MR1616583
10. [10] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer, Berlin, Heidelberg, New York (1991). Zbl0788.73002MR1115205
11. [11] A. Buffa, Hodge decompositions on the boundary of a polyhedron: the multi-connected case. Math. Models Methods Appl. Sci. 11 (2001) 1491–1504. Zbl1014.58002
12. [12] A. Buffa, Traces for functional spaces related to Maxwell equations: an overview, in Proceedings of GAMM-Workshop, Kiel (2001). 
13. [13] A. Buffa and P. Ciarlet Jr., On traces for functional spaces related to Maxwell’s equation. Part I: An integration by parts formula in lipschitz polyhedra. Math. Methods Appl. Sci. 24 (2001) 9–30. Zbl0998.46012
14. [14] A. Buffa, M. Costabel and D. Sheen, On traces for $𝐇(rot,\Omega )$ in Lipschitz domains. University of Pavia, IAN–CNR 1185 (2000). Zbl1106.35304
15. [15] A. Buffa, M. Costabel and Ch. Schwab, Boundary element methods for Maxwell’s equations on non-smooth domains. Numer. Math. (2001) (electronic) DOI 10.1007/s002110100372. Zbl1019.65094
16. [16] M. Costabel, Symmetric methods for the coupling of finite elements and boundary elements, in The Mathematics of Finite Elements and Applications IV, Academic Press, London (1988). Zbl0682.65069MR956899
17. [17] R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 5. Masson, Paris, Milan, Barcelone (1988). Zbl0749.35005MR944303
18. [18] G.N. Gatica and G.C. Hsiao, Boundary-field equation methods for a class of nonlinear problems. Longman (1995). Zbl0832.65126MR1379331
19. [19] V. Girault and P.A. Raviart, Finite element approximation of the Navier-Stokes equations: theory and algorithms. Springer, Berlin, Heidelberg, New York (1986). Zbl0413.65081MR851383
20. [20] R. Hiptmair, Symmetric coupling for eddy current problems. SIAM J. Numer. Anal. 40 (2002) 41–65. Zbl1010.78011
21. [21] C. Johnson and J.C. Nédélec, On the coupling of boundary integral and finite element methods. Math. Comp. 35 (1980) 1063–1079. Zbl0451.65083
22. [22] W. McLean, Strongly elliptic systems and boundary integral equations. Cambridge University Press (2000). Zbl0948.35001MR1742312
23. [23] S. Meddahi, An optimal iterative process for the Johnson-Nedelec method of coupling boundary and finite elements. SIAM J. Numer. Anal. 35 (1998) 1393–1415. Zbl0912.65096
24. [24] S. Meddahi, A mixed-FEM and BEM coupling for a two-dimensional eddy current problem. Numer. Funct. Anal. Optim. 22 (2001) 675–696. Zbl0996.78013
25. [25] S. Meddahi and F.J. Sayas, A fully discrete BEM-FEM for the exterior Stokes problem in the plane. SIAM J. Numer. Anal. 37 (2000) 2082–2102. Zbl0981.65129
26. [26] S. Meddahi, J. Valdés, O. Menéndez and P. Pérez, On the coupling of boundary integral and mixed finite element methods. J. Comput. Appl. Math. 69 (1996) 127–141. Zbl0854.65103
27. [27] J.C. Nédélec, Mixed finite elements in ${ℝ}^3$. Numer. Math. 35 (1980) 315–341. Zbl0419.65069
28. [28] J.C. Nédélec, Acoustic and electromagnetic equations. Integral representations for harmonic problems. Springer-Verlag, New York (2001). Zbl0981.35002MR1822275
29. [29] J.E. Roberts and J.M. Thomas, Mixed and hybrid methods, in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1991) 523–639. Zbl0875.65090