Weak solvability of interior transmission problems via mixed finite elements and Dirichlet-to-Neumann mappings

Journal of Computational and Applied Mathematics

Volumn 100, Issue 2, 1998, Pages 145-160

  Barrenechea, Gabriel R ^a   Gatica, Gabriel N ^a   Hsiao, George C ^b  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

Boundary integral method; Dirichlet to Neumann mapping; Mixed finite element; Non conforming Galerkin scheme; Transmission problem

Indexed keywords

APPROXIMATION THEORY; CONFORMAL MAPPING; FINITE ELEMENT METHOD; GALERKIN METHODS;

DIRICHLET TO NEUMANN MAPPINGS; MIXED FINITE ELEMENTS; TRANSMISSION PROBLEM; WEAK SOLVABILITY;

PROBLEM SOLVING;

EID: 0032298986     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00185-X     Document Type: Article

References (20)

1. G.R. Barrenechea, G.N. Gatica, On the coupling of boundary integral and finite element methods with nonlinear transmission conditions, Appl. Anal. 62 (1996a) 181-210.
2. G.R. Barrenechea, G.N. Gatica, On the weak solvability of interface problems through mixed finite elements and Dirichlet-to-Neumann methods, Technical Report 96-11, Departamento de Ingeniería Matemática, Universidad de Concepción, J. Math. Anal. Appl. (1996b) submitted.
3. F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, Berlin, 1991.
4. F. Brezzi, C. Johnson, On the coupling of boundary integral and finite element methods, Calcolo 16 (1979) 189-201.
5. M. Costabel, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988) 613-626.
6. M. Costabel, E.P. Stephan, Coupling of finite and boundary element methods for an elasto-plastic interface problem, SIAM J. Numer. Anal. 27(5) (1990) 1212-1226.
7. G.N. Gatica, On an alternative variational formulation for the Johnson & Nedelec's coupling procedure, Rev. Mat. Apl. 16 (1995) 17-41.
8. G.N. Gatica, Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity, Appl. Math. Lett. 10 (1997) 29-35.
9. G.N. Gatica, G.C. Hsiao, The uncoupling of boundary integral and finite element methods for nonlinear boundary value problems. J. Math. Anal. Appl. 189(2) (1995a) 442-461.
10. G.N. Gatica, G.C. Hsiao, Boundary-Field Equation Methods for a Class of Nonlinear Problems, Pitman Research Notes in Mathematics Series, vol. 331, Longman, New York 1995b.
11. G.N. Gatica, W.L. Wendland, Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems, Appl. Anal. 63 (1996) 39-75.
12. G.N. Gatica, W.L. Wendland, Coupling of mixed finite elements and boundary elements for a hyperelastic interface problem, SIAM J. Numer. Anal. 34 (1997) 2335-2356.
13. G.N. Gatica, W.L. Wendland, Coupling of mixed finite elements and boundary elements in potential theory and elastostatics, Z. Angew. Math. Mech. 75(S2) (1996) 525-526.
14. G.N. Gatica, W.L. Wendland, On the coupling of mixed finite element and boundary integral methods for a nonlinear elasticity problem, in: L. Morino, W.L. Wendland (Eds.), IABEM Symp. on Boundary Integral Methods for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1997, pp. 75-80.
15. V. Girault, P.A. Raviart, Finite Element Methods for the Navier-Stokes Equations. Theory and Algorithms, Springer, Berlin, 1986.
16. H. Han, X. Wu, The approximation of the exact boundary conditions at an artificial boundary for linear elastic equations and its applications, Math. Comput. 59 (1992) 21-37.
17. G.C. Hsiao, W.L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl. 58 (1977) 449-481.
18. G.C. Hsiao, S. Zhang, Optimal order multigrid methods for solving exterior boundary value problems, SIAM J. Numer. Anal. 31(3) (1994) 680-694.
19. J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, vol. I, Springer, Berlin, 1972.
20. J. Necas, Introduction to the Theory of Nonlinear Elliptic Equations, Wiley, New York, 1986.