A finite element method on composite grids based on Nitsche's method

Mathematical Modelling and Numerical Analysis

Volumn 37, Issue 3, 2003, Pages 495-514

  Hansbo, Anita ^a   Hansbo, Peter ^b   Larson, Mats G ^b  

^a UNIVERSITY WEST   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Nitsche's method; Overlapping grids

Indexed keywords

EID: 0038041040     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2003039     Document Type: Article

References (14)

1. Y. Achdou and Y. Maday, The mortar element method with overlapping subdomains. SIAM J. Numer. Anal. 40 (2002) 601-628.
2. R. Becker, P. Hansbo and R. Stenberg, A finite element method for domain decomposition with non-matching grids. ESAIM: M2AN 37 (2003) 209-225.
3. M.J. Berger, On conservation at grid interfaces. SIAM J. Numer. Anal. 24 (1987) 967-984.
4. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, Berlin (1994).
5. F. Brezzi, J.-L. Lions and O. Pironneau, Analysis of a Chimera method. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 655-660.
6. X.-C. Cai, M. Dryja and M. Sarkis, Overlapping nonmatching grid mortar element methods for elliptic problems. SIAM J. Numer. Anal. 36 (1999) 581-606.
7. G. Chesshire and W.D. Henshaw, Composite overlapping meshes for the solution of partial-differential equations. J. Comput. Phys. 90 (1990) 1-64.
8. V. Girault and P.-A. Raviart, Finite Element Approximation of the Navier-Stokes Equations. Springer-Verlag, Berlin (1979).
9. A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 5537-5552.
10. R.D. Lazarov, J.E. Pasciak, J. Schöberl and P.S. Vassilevski, Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids. Technical Report, ISC-01-05-MATH (2001).
11. R.D. Lazarov, S.Z. Tomov and P.S. Vassilevski, Interior penalty discontinuous approximations of elliptic problems, Comput. Meth. Appl. Math. 1 (2001) 367-382.
12. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9-15.
13. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 190 (1990) 483-493.
14. R. Stenberg, Mortaring by a method of J. A. Nitsche, in Computational Mechanics: New Trends and Applications, S. Idelsohn, E. Onate and E. Dvorkin Eds., CIMNE, Barcelona (1998).