New interpolation results and applications to finite element methods for elliptic boundary value problems

Journal of Numerical Mathematics

Volumn 9, Issue 3, 2001, Pages 179-198

  Bacutaf, C ^a   Bramble, J H ^a   Pasciak, J E ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

extension operator; finite element method; interpolation spaces

Indexed keywords

BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; GEOMETRY; MATHEMATICAL OPERATORS; VARIATIONAL TECHNIQUES;

DIRICHLET PART; EXTENSION OPERATOR; INTERPOLATION SPACES; POLYGONAL DOMAIN;

INTERPOLATION;

EID: 0035173823     PISSN: 15702820     EISSN: None     Source Type: Journal    
DOI: 10.1515/JNMA.2001.179     Document Type: Article

References (13)

1. C. Bacuta, J. H. Bramble, and J. Pasciak, Using Finite Element Tools in Proving Shift Theorems for Elliptic Boundary Value Problems (in preparation).
2. D. Braess, Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge, 1997.
3. J. H. Bramble, Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory. Math. Comp. (1995) 64, 1359-1365.
4. J. H. Bramble, R. Lazarov, and J. Pasciak, Least-squares for second-order elliptic problems. Comp. Meth. Appl. Mech. Engrg. (1998) 152, 195-210.
5. J. H. Bramble, R. Lazarov, and J. Pasciak, A least-squares approach based on a discrete minus one inner product for first order systems. Math. Comp. (1993) 60,447-471, Math. Comp. (1997) 66, 935-955.
6. J. H. Bramble, J. Pasciak, and P. S. Vassilevski, Computational scales of Sobolev norms with applications to preconditioning. Math. Comp. (2000) 69, 463-480.
7. S. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods. SpringerVerlag, New York, 1994.
8. P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland, Amsterdam, 1978.
9. V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations. SpringerVerlag, Berlin, 1986.
10. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston, 1985.
11. P. Grisvard, Singularities in Boundary Value Problems. Masson, Paris, 1992.
12. J.-L. Lions and E.Magenes, Non-homogeneous Boundary Value Problems and Applications, I. Springer-Verlag, New York, 1972.
13. J.-L. Lions and P. Peetre, Sur une classe d'espaces d'interpolation. Institut des Hautes Etudes Scientifique. Publ. Math. (1964) 19, 5-68.