Uniform a priori estimates for elliptic and static maxwell interface problems

Discrete and Continuous Dynamical Systems - Series B

Volumn 7, Issue 1, 2007, Pages 145-170

  Huang, Jianguo ^a,b   Zou, Jun ^c  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b University of Shanghai   (China)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

A priori estimates; Elliptic interface problem; Maxwell interface problem

Indexed keywords

EID: 33847714059     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.7.145     Document Type: Article

References (28)

1. R. Adams, "Sobolev Spaces," Academic Press, New York, 1975.
2. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains, Math. Meth. Appl. Sci., 21(1998), 823-864.
3. T. Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer, Berlin, 1998.
4. I. Babuska, The finite element method for elliptic equations with discontinuous coefficients, Computing, 5 (1970), 207-213.
5. G. Chen and J. Zhou, "Boundary Element Methods," Academic Press, London, 1992.
6. Z. Chen, Q. Du and J. Zou, Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients, SIAM J. Numer. Anal., 37 (2000), 1542-1570.
7. E. T. Chung, Q. Du and J. Zou, Convergence analysis of a finite volume method for Maxwell's equations in nonhomogeneous media, SIAM J. Numer. Anal., 41 (2003), 37-63.
8. 2AN, 33(1999), 627-649.
9. R. Dautray and J. Lions, "Mathematical Analysis and Numerical Methods for Science and Technology," Springer, Berlin, 1988.
10. G. Duvaut and J. Lions, "Inequalities in Mechanics and Physics," Springer, Berlin, 1976.
11. D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin-New York, 2001.
12. V. Girault and P. Raviart, "Finite Element Methods for the Navier-Stokes Equations, Theory and Algorithms," Springer, Berlin, 1986.
13. P. Grisvard, "Elliptic Problems in Nonsmooth Domains," Pitman Advanced Publishing Program, Boston, 1985.
14. R. Hiptmair, Finite elements in computational electromagnetism, Acta Numerica, 2002, 237-339.
15. J. Huang and J. Zou, Some new a priori estimates for second-order elliptic and parabolic interface problems, J. Diff. Eqn., 184 (2002), 570-586.
16. H. Kang, J. Seo and D. Sheen, Numerical identification of discontinuous conductivity coefficients, Inverse Problems, 13 (1997), 113-123.
17. R. Kellogg, Singularities in interface problems, in "Numerical Solution of Partial Differential Equations," II, Academic Press, New York, 1971.
18. C. Kenig, "Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems," CBMS No. 83, AMS, Providence, Phode Island, 1994.
19. T. Li and T. Qin, "Physics and Partial Differential Equations (I) (in Chinese)," Chinese Advanced Education Press, Beijing, 1997.
20. Y. Li and L. Nirenberg, Estimates for elliptic systems from composite material, Comm. Pure Appl. Math., LVI(2003), 892-925.
21. J. Lions, "Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal," Springer, Berlin, Lecture Notes in Mathematics 323, 1973.
22. J. Lions and E. Magenes, "Nonhomeneous Boundary Value Problems and Applications, I, II," Springer, Berlin, 1972-1973.
23. M. Plum and C. Wieners, Optimal a priori estimates for interface problems, Numer. Math., 95(2003), 735-759.
24. M. Protter and H. Weiberger, "Maximum Principles in Differential Equations," Prentice-Hall, Englewood Cliffs, NJ, 1967.
25. M. Taylor, "Tools for PDE: pseudodifferential operators, paradifferential operators, and layer potentials," AMS, Providence, RI, 2000.
26. G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains, J. Funct. Anal., 59 (1984), 572-611.
27. J. Xu and J. Zou, Some nonoverlapping domain decomposition methods, SIAM Review, 40 (1998), 857-914.
28. J. Zhao, "Analysis of Finite Element Approximation and Iterative Methods for Time-dependent Maxwell Problems", Ph. D. Thesis, Department of Mathematics, Texas A & M University, 2002.