On the convergence of finite element method for second order elliptic interface problems

Numerical Functional Analysis and Optimization

Volumn 27, Issue 1, 2006, Pages 99-115

  Sinha, Rajen Kumar ^a   Deka, Bhupen ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

Elliptic equation; Finite element method; Interface; Optimal error estimates; Quadrature

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING;

ELLIPTIC EQUATION; INTERFACE; OPTIMAL ERROR ESTIMATES; QUADRATURE;

FINITE ELEMENT METHOD;

EID: 33645012045     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560500538821     Document Type: Article

References (16)

1. R.A. Adams (1975). Sobolev Spaces. Academic Press, New York.
2. I. Babuska (1970). The finite element method for elliptic equations with discontinuous coefficients. Computing 5:207-213.
3. J.W. Barrett and C.M. Elliott (1987). Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. IMA J. Numer. Anal. 7:283-300.
4. J.H. Bramble, J.E. Pasciak, and A.H. Schatz (1986). An iterative method for elliptic problems on regions partitioned into substructures. Math. Comp. 46:361-369.
5. J.H. Bramble, J.E. Pasciak, and A.H. Schatz (1986). The construction of preconditioners for elliptic problems by substructuring I. Math. Comp. 47:103-134.
6. S.C. Brenner and L.R. Scott (1994). The Mathematical Theory of Finite Element Methods. Springer-Verlag.
7. Z. Chen and J. Zou (1998). Finite element methods and their convergence for elliptic and parabolic interface problems. Numer. Math. 79:175-202.
8. P.G. Ciarlet (1978). The Finite Element Method for Elliptic Problems. North Holland, Amsterdam.
9. W. Hackbusch (1992). Elliptic Differential Equations. Theory and Numerical Treatment. Springer-Verlag, New York, Berlin.
10. J. Huang and J. Zou (2002). A mortar element method for elliptic problems with discontinuous coefficients. IMA J. Numer. Anal. 22:554-576.
11. O.A. Ladyzhenskaya, V.Ja. Rivkind, and N.N. Ural'ceva (1966). The classical solvability of diffraction problems. Trudy Mat. Inst. Steklov 92:116-146.
12. Translated in Proc. Steklov Institute Math. 92 (1966); Boundary value problems of mathematical physics IV, Am. Math. Soc.
13. B.F. Nielsen (1999). Finite element discretizations of elliptic problems in the presence of arbitrarily small ellipticity: An error analysis. SIAM J. Numer. Anal. 36:368-392.
14. Z. Li, T. Lin, and X.H. Wu (2003). New Cartesian grid methods for interface problems using the finite element formulation. Numer. Math. 96:61-98.
15. M. Plum and C. Wieners (2003). Optimal a priori estimates for interface problems. Numer. Math. 95:735-759.
16. J. Xu (1982). Error estimates of the finite element method for the 2nd order elliptic equations with discontinuous coefficients. J. Xiangtan University 1:1-5.