Optimal a priori estimates for interface problems

Numerische Mathematik

Volumn 95, Issue 4, 2003, Pages 735-759

  Plum, Michael ^a   Wieners, Christian ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242308001     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110200395     Document Type: Article

References (15)

1. Babuška, I., Caloz, C., Osborn, J.: Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal., 31, 945-981 (1994)
2. Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuss, N., Rentz-Reichert, H., Wieners, C.: UG - a flexible software toolbox for solving partial differential equations. Computing and Visualization in Science, 1, 27-40 (1997)
3. Berkowitz, J.: On the discreteness of spectra of singular Sturm-Liouville problems. Comm. Pure and Appl. Math., 12, 523-542 (1959)
4. Bernstein, S. N.: Sur la généralisation du problème de Dirichlet. Math. Ann., 69, 82-132 (1910)
5. Bramble, J. H., Pasciak, J. E., Wang, J., Xu, J.: Convergence estimates for multgrid algorithms without regularity assumptions. Math. Comp., 57, 23-45 (1991)
6. Brenner, S. C.: Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities. Math. Comp., 68, 559-583 (1999)
7. 2-metric. Tr. Mat. Inst. Steklov, 77, 160-191 (1965)
8. Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Pitman, Boston, 1985
9. Ladyzhenskaya, O., Uraltseva, N.: Linear and Quasilinear Elliptic Equations. Academic Press, New York, 1968
10. Lemrabet, K.: Régularité de la solution d'un problème de transmission. J. Math. pures et appl., 56, 1-38 (1977)
11. Neuss, N.: Homogenisierung und Mehrgitterverfahren. PhD thesis, Universität Heidelberg, 1995
12. Neuss, N., Wieners, C.: Criteria for the approximation property for multigrid methods in nonnested spaces. (2000). Submitted
13. Nicaise, S.: Polygonal Interface Problems, vol. 39 of Methoden und Verfahren der Mathematischen Physik. Verlag Peter D. Lang, Frankfurt a. M., 1993
14. 2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems. J. Math. Anal. Appl., 165, 36-61 (1992)
15. Wang, J.: New convergence estimates for multilevel algorithms for finite element approximations. J. Comput. Appl. Math., 50, 593-604 (1994)