Free Access
Issue
ESAIM: M2AN
Volume 34, Number 1, January/February 2000
Page(s) 159 - 182
DOI https://doi.org/10.1051/m2an:2000136
Published online 15 April 2002
  1. B. Achchab, A. Agouzal, J. Baranger and J. Maitre, Estimateur d'erreur a posteriori hiérarchique. Application aux éléments finis mixtes. IMPACT Comput. Sci. Engrg. 1 (1995) 3-35. [Google Scholar]
  2. R. Albanese and G. Rubinacci, Formulation of the eddy-current problem. IEE Proc. A 137 (1990) 16-22. [Google Scholar]
  3. Analysis of three dimensional electromagnetic fileds using edge elements. J. Comp. Phys. 108 (1993) 236-245. [Google Scholar]
  4. A. Alonso and A. Valli, Some remarks on the characterization of the space of tangential traces of H(rot;Ω) and the construction of an extension operator. Manuscripta math. 89 (1996) 159-178. [Google Scholar]
  5. H. Ammari, A. Buffa and J.-C. Nédélec, A justification of eddy currents model for the Maxwell equations. Tech. Rep., IAN, University of Pavia, Pavia, Italy (1998). [Google Scholar]
  6. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional nonsmooth domains. Math. Methods Appl. Sci. 21 (1998) 823-864. [CrossRef] [MathSciNet] [Google Scholar]
  7. D. Arnold, A. Mukherjee and L. Pouly, Locally adapted tetrahedral meshes using bisection. SIAM J. on Sci. Compt (submitted). [Google Scholar]
  8. I. Babuska and W. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736-754. [CrossRef] [MathSciNet] [Google Scholar]
  9. I. Babuska and W. Rheinboldt, A posteriori error estimates for the finite element method. Internet. J. Numer. Methods Engrg. 12 (1978) 1597-1615. [Google Scholar]
  10. R. Bank, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, User's Guide 6.0. SIAM, Philadelphia (1990). [Google Scholar]
  11. R. Bank, A. Sherman and A. Weiser, Refinement algorithm and data structures for regular local mesh refinement., in Scientific Computing, R. Stepleman et al., Ed., Vol. 44, IMACS North-Holland, Amsterdam (1983) 3-17. [Google Scholar]
  12. R. Bank and A. Weiser, some a posteriori error estimators for elliptic partial differential equations. Math. Comp. 44 (1985) 283-301. [Google Scholar]
  13. E. Bänsch, Local mesh refinement in 2 and 3 dimensions. IMPACT Comput. Sci. Engrg. 3 (1991) 181-191. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Beck, P. Deuflhard, R. Hiptmair, R. Hoppe and B. Wohlmuth, Adaptive multilevel methods for edge element discretizations of Maxwell's equations. Surveys for Mathematics in Industry. [Google Scholar]
  15. R. Beck and R. Hiptmair, Multilevel solution of the time-harmonic Maxwell equations based on edge elements. Tech. Rep. SC-96-51, ZIB Berlin (1996). in Internat. J. Numer. Methods Engrg. (To appear). [Google Scholar]
  16. J. Bey, Tetrahedral grid refinement. Computing 55 (1995) 355-378. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Bornemann, An adaptive multilevel approach to parabolic equations I. General theory and 1D-implementation. IMPACT Comput. Sci. Engrg. 2 (1990) 279-317. [CrossRef] [Google Scholar]
  18. F. Bornemann, An adaptive multilevel approach to parabolic equations II. Variable-order time discretization based on a multiplicative error correction. IMPACT Comput. Sci. Engrg. 3 (1991) 93-122. [CrossRef] [MathSciNet] [Google Scholar]
  19. F. Bornemann, B. Erdmann and R. Kornhuber, A posteriori error estimates for elliptic problems in two and three spaces dimensions. SIAM J. Numer. Anal. 33 (1996) 1188-1204. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Bossavit, Mixed finite elements and the complex of Whitney forms, in The Mathematics of Finite Elements and Applications VI J. Whiteman Ed., Academic Press, London (1988) 137-144. [Google Scholar]
  21. A. Bossavit, A rationale for edge elements in 3D field computations. IEEE Trans. Mag. 24 (1988) 74-79. [Google Scholar]
  22. A. Bossavit, Solving Maxwell's equations in a closed cavity and the question of spurious modes. IEEE Trans. Mag. 26 (1990) 702-705. [CrossRef] [Google Scholar]
  23. A. Bossavit, Électromagnétisme, en vue de la modélisation. Springer-Verlag, Paris (1993). [Google Scholar]
  24. A. Bossavit, Computational Electromagnetism. Variational Formulation, Complementarity, Edge Elements.in Academic Press Electromagnetism Series, no. 2 Academic Press, San Diego (1998). [Google Scholar]
  25. D. Braess and R. Verfürth, A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431-2445. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Carstensen, A posteriori error estimate for the mixed finite element method. Math. Comp. 66 (1997) 465-476. [Google Scholar]
  27. P. Ciarlet, The Finite Element Method for Elliptic Problems. Studies in Mathematics and its Applications, Vol. 4 North-Holland, Amsterdam (1978). [Google Scholar]
  28. M. Clemens, R. Schuhmann, U. van Rienen and T. Weiland, Modern Krylov subspace methods in electromagnetic field computation using the finite integration theory. ACES J. Appl. Math. 11 (1996) 70-84. [Google Scholar]
  29. M. Clemens and T. Weiland, Transient eddy current calculation with the FI-method. in Proc. CEFC '98, IEEE (1998); IEEE Trans. Mag. submitted [Google Scholar]
  30. P. Clément, Approximation by finite element functions using local regularization. Revue Franc. Automat. Inform. Rech. Operat. 9, R-2 (1975) 77-84. [Google Scholar]
  31. M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains. Tech. Rep. 97-19, IRMAR, Rennes, France (1997). [Google Scholar]
  32. M. Costabel, M. Dauge and S. Nicaise, Singularities of Maxwell interface problems, Tech. Rep. 98-24, IRMAR, Rennes, France (1998). [Google Scholar]
  33. H. Dirks, Quasi-stationary fields for microelectronic applications. Electrical Engineering 79 (1996) 145-155. [CrossRef] [Google Scholar]
  34. P. Dular, J.-Y. Hody, A. Nicolet, A. Genon and W. Legros, Mixed finite elements associated with a collection of tetrahedra, hexahedra and prisms. IEEE Trans Magnetics MAG-30 (1994) 2980-2983. [Google Scholar]
  35. K. Erikson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations. Acta Numerica 4 (1995) 105-158. [CrossRef] [Google Scholar]
  36. K. Eriksson and C. Johnson, An adaptive finite element method for linear elliptic problems. Math. Comp. 50 (1988) 361-383. [CrossRef] [MathSciNet] [Google Scholar]
  37. V. Girault and P. Raviart, Finite element methods for Navier-Stokes equations, Springer-Verlag, Berlin (1986). [Google Scholar]
  38. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin, Heidelberg, New York (1991). [Google Scholar]
  39. R. Hiptmair, Multigrid method for Maxwell's equations. Tech. Rep. 374, Institut für Mathematik, Universität Augsburg (1997). [Google Scholar]
  40. R. Hiptmair, Canonical construction of finite elements. Math. Comp. 68 (1999) 1325-1346. [Google Scholar]
  41. R. Hoppe and B. Wohlmuth, Adaptive multilevel iterative techniques for nonconforming finite element discretizations. East-West J. Numer. Math. 3 (1995) 179-197. [MathSciNet] [Google Scholar]
  42. R. Hoppe and B. Wohlmuth, A comparison of a posteriori error estimators for mixed finite elements. Math. Comp. 68 (1999) 1347-1378. [CrossRef] [MathSciNet] [Google Scholar]
  43. R. Hoppe and B. Wohlmuth, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods. Model. Math. Anal. Numér. 30 (1996) 237-263. [Google Scholar]
  44. R. Hoppe and B. Wohlmuth, Adaptive multilevel techniques for mixed finite element discretizations of elliptic boundary value problems. SIAM J. Numer. Anal. 34 (1997) 1658-1687. [CrossRef] [MathSciNet] [Google Scholar]
  45. R. Hoppe and B. Wohlmuth, Hierarchical basis error estimators for Raviart-Thomas discretizations of arbitrary order, in Finite Element Methods: Superconvergence, Post-processing and A Posteriori Estimates, M. Krizck, P. Neittaanmäki and R. Stenberg Eds., Marcel Dekker, New York (1997) 155-167. [Google Scholar]
  46. J. Maubach, Local bisection refinement for n-simplicial grids generated by reflection. SIAM J. Sci. Stat. Comp. 16 (1995) 210-227. [CrossRef] [Google Scholar]
  47. P. Monk, A mixed method for approximating Maxwell's equations. SIAM J. Numer. Anal. 28 (1991) 1610-1634. [CrossRef] [MathSciNet] [Google Scholar]
  48. P. Monk, Analysis of a finite element method for Maxwell's equations. SIAM J. Numer. Anal. 29 (1992) 714-729. [CrossRef] [MathSciNet] [Google Scholar]
  49. J. Nédélec, Mixed finite elements in R3, Numer. Math. 35 (1980) 315-341. [CrossRef] [MathSciNet] [Google Scholar]
  50. E. Ong, Hierarchical basis preconditioners for second order elliptic problems in three dimensions. Ph.D. thesis, Dept. of Math., UCLA, Los Angeles, CA, USA (1990). [Google Scholar]
  51. P. Oswald, Multilevel finite element approximation. Teubner Skripten zur Numerik, B.G. Teubner, Stuttgart (1994). [Google Scholar]
  52. J. P. Ciarlet and J. Zou, Fully discrete finite element approaches for time-dependent Maxwell equations. Tech. Rep. TR MATH-96-31 (105), Department of Mathematics, The Chinese University of Hong Kong (1996). Num. Math. (to appear). [Google Scholar]
  53. L. R. Scott and Z. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483-493. [Google Scholar]
  54. R. Verfürth, A posteriori error estimators for nonlinear problems. Finite element discretizations of elliptic equations. Math. Comp. 62 (1994) 445-475. [MathSciNet] [Google Scholar]
  55. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, Chichester, Stuttgart (1996). [Google Scholar]
  56. H. Whitney, Geometric Integration Theory. Princeton Univ. Press, Princeton (1957). [Google Scholar]
  57. J. Zhu and O. Zienkiewicz, Adaptive techniques in the finite element method. Commun. Appl. Numer. Methods 4 (1988) 197-204. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you