Free access
Issue
ESAIM: M2AN
Volume 36, Number 2, March/April 2002
Page(s) 241 - 272
DOI http://dx.doi.org/10.1051/m2an:2002011
Published online 15 May 2002
  1. M. Ainsworth and J.T. Oden, A unified approach to a posteriori error estimation using element residual methods. Numer. Math. 65 (1993) 23-50. [CrossRef] [MathSciNet]
  2. I. Babuska and A.K. Aziz, Survey lectures on the mathematical foundations of the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz Ed., Academic Press, New York (1972).
  3. R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations. Math. Comp. 44 (1985) 283-301. [CrossRef] [MathSciNet]
  4. M.A. Barrientos, A-posteriori Error Analysis of Dual-Mixed Variational Formulations for Linear and Nonlinear Boundary Value Problems (spanish). Ph.D. thesis, Universidad de Concepción, Concepción, Chile (in preparation).
  5. M.A. Barrientos, G.N. Gatica and N. Heuer, An a-posteriori error estimate for a linear-nonlinear transmission problem in plane elastostatics. Technical Report 00-11, Departamento de Ingeniería Matemática, Universidad de Concepción (2000). Calcolo (to appear).
  6. M.A. Barrientos, G.N. Gatica and E.P. Stephan, A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate. Technical Report 99-25, Departamento de Ingeniería Matemática, Universidad de Concepción (1999). Numer. Math. (to appear).
  7. C. Bernardi, Optimal finite-element interpolation on curved domains. SIAM J. Numer. Anal. 26 (1989) 1212-1240.
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, Berlin, Heidelberg, New York (1991).
  9. U. Brink, C. Carstensen and E. Stein, Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics. Numer. Math. 75 (1996) 153-174. [CrossRef] [MathSciNet]
  10. C. Carstensen, A posteriori error estimate for the symmetric coupling of finite elements and boundary elements. Computing 57 (1996) 301-322. [CrossRef] [MathSciNet]
  11. C. Carstensen, An a-posteriori error estimate for a first-kind integral equation. Math. Comp. 66 (1997) 139-155. [CrossRef] [MathSciNet]
  12. C. Carstensen and S.A. Funken, Coupling of mixed finite elements and boundary elements. IMA J. Numer. Anal. 20 (2000) 461-480.
  13. C. Carstensen, S.A. Funken and E.P. Stephan, On the adaptive coupling of FEM and BEM in 2-d-elasticity. Numer. Math. 77 (1997) 187-221. [CrossRef] [MathSciNet]
  14. C. Carstensen and E.P. Stephan, Adaptive coupling of boundary elements and finite elements. RAIRO Modél. Math. Anal. Numér. 29 (1995) 779-817. [MathSciNet]
  15. P. Clément, Approximation by finite element functions using local regularisation. RAIRO Anal. Numér. 9 (1975) 77-84.
  16. G.N. Gatica, Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity. Appl. Math. Lett. 10 (1997) 29-35. [CrossRef] [MathSciNet]
  17. G.N. Gatica, An application of Babuska-Brezzi's theory to a class of variational problems. Appl. Anal. 75 (2000) 297-303. [CrossRef] [MathSciNet]
  18. G.N. Gatica and N. Heuer, A dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity. SIAM J. Numer. Anal. 38 (2000) 380-400.
  19. G.N. Gatica, N. Heuer and E.P. Stephan, An implicit-explicit residual error estimator for the coupling of dual-mixed finite elements and boundary elements in elastostatics. Math. Methods Appl. Sci. 24 (2001) 179-191. [CrossRef] [MathSciNet]
  20. G.N. Gatica and G.C. Hsiao, The uncoupling of boundary integral and finite element methods for nonlinear boundary value problems. J. Math. Anal. Appl. 189 (1995) 442-461. [CrossRef] [MathSciNet]
  21. G.N. Gatica and S. Meddahi, An a-posteriori error estimate for the coupling of BEM and mixed-FEM. Numer. Funct. Anal. Optim. 20 (1999) 449-472. [CrossRef] [MathSciNet]
  22. G.N. Gatica and S. Meddahi, A dual-dual mixed formulation for nonlinear exterior transmission problems. Math. Comp. 70 (2001) 1461-1480. [CrossRef] [MathSciNet]
  23. G.N. Gatica and E.P. Stephan, A mixed-FEM formulation for nonlinear incompressible elasticity in the plane. Numer. Methods for Partial Differential Equations 18 (2002) 105-128. [CrossRef]
  24. G.N. Gatica and W.L. Wendland, Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems. Appl. Anal. 63 (1996) 39-75. [CrossRef] [MathSciNet]
  25. G.N. Gatica and W.L. Wendland, Coupling of mixed finite elements and boundary elements for a hyperelastic interface problem. SIAM J. Numer. Anal. 34 (1997) 2335-2356.
  26. D. Givoli, Numerical Methods for Problems in Infinite Domains. Elsevier Science Publishers B.V. (1992), Studies in Applied Mechanics 33.
  27. P. Grisvard, Elliptic Problems in Non-Smooth Domains. Monographs and Studies in Mathematics, Vol. 24, Pitman (1985).
  28. H. Han and W. Bao, The artificial boundary conditions for incompressible materials on an unbounded domain. Numer. Math. 77 (1997) 347-363. [CrossRef] [MathSciNet]
  29. H. Han and X. Wu, The approximation of the exact boundary conditions at an artificial boundary for linear elastic equations and its application. Math. Comp. 59 (1992) 21-37. [MathSciNet]
  30. G.C. Hsiao and S. Zhang, Optimal order multigrid methods for solving exterior boundary value problems. SIAM J. Numer. Anal. 31 (1994) 680-694.
  31. R. Kress, Linear Integral Equations. Springer-Verlag (1989).
  32. S. Meddahi, J. Valdés, O. Menéndez and P. Pérez, On the coupling of boundary integral and mixed finite element methods. J. Comput. Appl. Math. 69 (1996) 113-124. [CrossRef] [MathSciNet]
  33. P. Mund and E.P. Stephan, An adaptive two-level method for the coupling of nonlinear FEM-BEM equations. SIAM J. Numer. Anal. 36 (1999) 1001-1021.
  34. J.E. Roberts and J.-M. Thomas, Mixed and Hybrid Methods, in Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions Eds., Vol. II, Finite Element Methods (Part 1), North-Holland, Amsterdam (1991).
  35. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, Chichester (1996).
  36. A. Zenisek, Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations. Academic Press, London (1990).

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