Adaptive finite element method for a coefficient inverse problem for Maxwell's system

References

• Engl , HW , Hanke , M and Neubauer , A . 2000 . Regularization of Inverse Problems , Boston : Kluwer Academic Publishers .
   Google Scholar
• U. Tautenhahn, Tikhonov regularization for identification problems in differential equations, in International Conference on Parameter Identification and Inverse problems in Hydrology, Geology and Ecology, Dodrecht, Kluwer, 1996, pp. 261–270.
   Google Scholar
• Tikhonov , AN , Goncharsky , AV , Stepanov , VV and Yagola , AG . 1995 . Numerical Methods for the Solution of Ill-Posed Problems , London : Kluwer .
   Google Scholar
• A. Griesbaum, B. Kaltenbacher and B. Vexler, Efficient computation of the Tikhonov regularization parameter by goal-oriented adaptive discretization, Inverse Probl. 24 (2008), p. 025025.
   Google Scholar
• Beilina , L and Johnson , C . 2005 . A posteriori error estimation in computational inverse scattering . Math. Models and Methods in Applied Sciences , 15 : 23 – 35 .
   Web of Science ®Google Scholar
• Beilina , L . 2003 . Adaptive finite element/difference method for inverse elastic scattering waves . Appl. Comput. Math. , 2 : 119 – 134 .
   Google Scholar
• Eriksson , K , Estep , D and Johnson , C . 1996 . Computational Differential Equations , Studentlitteratur : Lund .
   Google Scholar
• Eriksson , K , Estep , D and Johnson , C . 1995 . Introduction to adaptive methods for differential equations . Acta Numeric. , 4 : 105 – 158 .
   Google Scholar
• C. Johnson, Adaptive computational methods for differential equations, ICIAM99, Oxford University Press, 2000, pp. 96–104.
   Google Scholar
• Beilina , L and Klibanov , MV . 2010 . A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem . Inverse Probl. , 26 : 045012
   Web of Science ®Google Scholar
• Beilina , L , Klibanov , MV and Kokurin , MYu . 2010 . Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem . J. Math. Sci. , 167 ( 3 ) : 279 – 325 .
   Google Scholar
• Ainsworth , M and Oden , J . 2000 . A Posteriori Error Estimation in Finite Element Analysis , New York : Wiley .
   Google Scholar
• Eriksson , K , Estep , D and Johnson , C . 2004 . Applied Mathematics: Body and Soul. Calculus in Several Dimensions , Berlin : Springer-Verlag .
   Google Scholar
• Repin , SI . 2008 . A Posteriori Estimates for Partial Differential Equations , Berlin : de Gruiter .
   Google Scholar
• Beilina , L and Johnson , C . 2001 . “ A Hybrid FEM/FDM Method for an Inverse Scattering Problem ” . In Numerical Mathematics and Advanced Applications – ENUMATH 2001 , Berlin : Springer-Verlag .
   Google Scholar
• Beilina , L and Clason , C . 2006 . An adaptive hybrid FEM/FDM method for an inverse scattering problem in scanning acoustic microscopy . SIAM J. Sci. Comp. , 28 : 382 – 402 .
   Web of Science ®Google Scholar
• Nédélec , JC . 1986 . A new family of mixed finite elements in ℝ3 . NUMMA , 50 : 57 – 81 .
   Web of Science ®Google Scholar
• Lee , RL and Madsen , NK . 1990 . A mixed finite element formulation for Maxwell's equations in the time domain . J. Comput. Physi. , 88 : 284 – 304 .
   Web of Science ®Google Scholar
• Paulsen , KD and Lynch , DR . 1991 . Elimination of vector parasities in finite element maxwell solutions . IEEE Trans. Microwave Theory Tech. , 39 : 395 – 404 .
   Web of Science ®Google Scholar
• M. J. Grote, A. Schneebeli, D. Sch´otzau, Interior penalty discontinuous Galerkin method for Maxwell s equations: Energy norm error estimates, J. Comput. Appli. Math., Elsevier Science Publishers, 204(2) (2007), pp. 375–386.
   Google Scholar
• Monk , PB . 2003 . Finite Element Methods for Maxwell's Equations , Loxford : Oxford University Press .
   Google Scholar
• Elmkies , A and Joly , P . 1997 . Finite elements and mass lumping for Maxwell's equations: the 2D case . Numeri. Anal., C. R. Acad. Sci. Paris , 324 : 1287 – 1293 .
   Google Scholar
• Joly , P . 2003 . “ Variational Methods for Time-dependent Wave Propagation Problems ” . In Lecture Notes in Computational Science and Engineering , Berlin : Springer-Verlag .
   Google Scholar
• Jin , J . 1993 . The Finite Element Methods in Electromagnetics , New York : Wiley .
   Google Scholar
• Brenner , SC and Scott , LR . 1994 . The Mathematical Theory of Finite Element Methods , Berlin : Springer-Verlag .
   Google Scholar
• Cohen , GC . 2002 . Highre Order Numerical Methods for Transient Wave Equations , Berlin : Springer-Verlag .
   Google Scholar
• Hughes , TJR . 1987 . The Finite Element Method , Englewoodceiffs, NJ : Prentice Hall .
   Google Scholar
• Becker , R . 2001 . Adaptive finite elements for optimal control problems , Universitat Heideberg : Habilitation thesis .
   Google Scholar
• Nocedal , J . 1991 . Updating quasi-Newton matrices with limited storage . Math. Comp. , 35 ( 151 ) : 773 – 782 .
   Google Scholar
• Pironneau , O . 1984 . Optimal Shape Design for Elliptic Systems , Berlin : Springer-Verlag .
   Google Scholar