Regularity estimates for elliptic boundary value problems in Besov spaces

Mathematics of Computation

Volumn 72, Issue 244, 2003, Pages 1577-1595

  Bacuta, Constantin ^a   Bramble, James H ^b   Xu, Jinchao ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Besov spaces; Finite element method; Interpolation spaces; Multilevel decomposition; Shift theorems

Indexed keywords

EID: 0141872538     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-02-01502-8     Document Type: Article

References (28)

1. R. A. Adams. Sobolev Spaces. Academic Press, New York, 1975. MR 56:9247
2. C. Bacuta, J. H. Bramble, J. Pasciak. New interpolation results and applications to finite element methods for elliptic boundary value problems. East-West J. Numer. Math. 9:179-198, 2001. MR 2002h:41053
3. C. Bennett and R. Sharpley. Interpolation of Operators. Academic Press, New-York, 1988. MR 89e:46001
4. J. Bergh, J. Löström. Interpolation Spaces. An Introduction, Springer-Verlag, New York, 1976. MR 58:2349
5. D. Braess. Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge, 1997. MR 98f:65002
6. J. H. Bramble. Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory. Math. Comp., 64:1359-1365, 1995. MR 95m:46042
7. J. H. Bramble and S. R. Hubert. Estimation of linear functional on Sobolev spaces with applications to Fourier transforms and spline interpolation. SIAM J. Numer. Anal., 7:113- 124, 1970. MR 41:7819
8. J. H. Bramble, J. Pasciak and P. S. Vassilevski. Computational scales of Sobolev norms with applications to preconditioning. Math. Comp., 69:463-480, 2000. MR 2000k:65088
9. J. H. Bramble, J. Pasciak and J.Xu. Parallel multilevel preconditioners. Math. Comp., 55:1-22, 1990. MR 90k:65170
10. J. H. Bramble and X. Zhang. The analysis of multigrid methods, in: Handbook for Numerical Analysis, Vol. VII, 173-415, P. Ciarlet and J.L. Lions, eds., North Holland, Amsterdam, 2000. MR 2001m:65183
11. S. Brenner and L.R. Scott. The Mathematical Theory of Finite Element Methods. Springer- Verlag, New York, 1994. MR 95f:65001
12. P. G. Ciarlet. The Finite Element Method for Elliptic Problems. North Holland, Amsterdam, 1978. MR 58:25001
13. M. Dauge. Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics 1341. Springer-Verlag, Berlin, 1988. MR 91a:35078
14. M. Dobrowolski. Numerical Approximation of Elliptic Interface and Corner Problems. Rheinischen Friedrich-Wilhelrns-Universität, Bonn,1981.
15. P. Grisvard. Elliptic Problems in Nonsmooth Domains. Pitman, Boston, 1985. MR 86m:35044
16. P. Grisvard. Singularities in Boundary Value Problems. Masson, Paris, 1992. MR 93h:35004
17. P. Grisvard. Caracterisation de quelques espaces d'interpolation. Arc. Rat. Mech. Anal. 25:40- 63, 1967. MR 35:4718
18. R. B. Kellogg. Interpolation between subspaces of a Hilbert space, Technical note BN-719. Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, 1971.
19. V. Kondratiev. Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc., 16:227-313, 1967. MR 37:1777
20. V. A. Kozlov, V. G. Mazya and J. Rossmann. Elliptic Boundary Value Problems in Domains with Point Singularities. American Mathematical Society, Mathematical Surveys and Monographs, vol. 52, 1997. MR 98f:35038
21. J. L. Lions and E. Magenes. Non-homogeneous Boundary Value Problems and Applications, I. Springer-Verlag, New York, 1972. MR 50:2670
22. J. L. Lions and P. Peetre. Sur une classe d'espaces d'interpolation. Institut des Hautes Etudes Scientifique. Publ. Math., 19:5-68, 1964. MR 29:2627
23. S. A. Nazarov and B. A. Plamenevsky. Elliptic Problems in Domains with Piecewise Smooth Boundaries. Expositions in Mathematics, vol. 13, de Gruyter, New York, 1994. MR 95h:35001
24. J. Nečas. Les Methodes Directes en Theorie des Equations Elliptiques. Academia, Prague, 1967. MR 37:3168
25. P. Oswald. Multilevel Finite Element Approximation. B. G. Teubner, Stuttgart, 1994. MR 95k:65110
26. 1 projections into finite element spaces: In fluence of a reentrant corner. Math. Comp., 42:1-8, 1984. MR 86b:65129
27. J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Review, 34:581-613, December 1992. MR 93k:65029
28. K. Yosida. Lectures on Differential and Integral Equations. Dover Publications, Inc., New York, 1991. MR 92a:34002