Free Access
Volume 36, Number 2, March/April 2002
Page(s) 241 - 272
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] [Google Scholar]
  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). [Google Scholar]
  3. R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations. Math. Comp. 44 (1985) 283-301. [Google Scholar]
  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). [Google Scholar]
  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). [Google Scholar]
  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). [Google Scholar]
  7. C. Bernardi, Optimal finite-element interpolation on curved domains. SIAM J. Numer. Anal. 26 (1989) 1212-1240. [Google Scholar]
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, Berlin, Heidelberg, New York (1991). [Google Scholar]
  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] [Google Scholar]
  10. C. Carstensen, A posteriori error estimate for the symmetric coupling of finite elements and boundary elements. Computing 57 (1996) 301-322. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Carstensen, An a-posteriori error estimate for a first-kind integral equation. Math. Comp. 66 (1997) 139-155. [CrossRef] [MathSciNet] [Google Scholar]
  12. C. Carstensen and S.A. Funken, Coupling of mixed finite elements and boundary elements. IMA J. Numer. Anal. 20 (2000) 461-480. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  15. P. Clément, Approximation by finite element functions using local regularisation. RAIRO Anal. Numér. 9 (1975) 77-84. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  26. D. Givoli, Numerical Methods for Problems in Infinite Domains. Elsevier Science Publishers B.V. (1992), Studies in Applied Mechanics 33. [Google Scholar]
  27. P. Grisvard, Elliptic Problems in Non-Smooth Domains. Monographs and Studies in Mathematics, Vol. 24, Pitman (1985). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  31. R. Kress, Linear Integral Equations. Springer-Verlag (1989). [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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). [Google Scholar]
  35. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, Chichester (1996). [Google Scholar]
  36. A. Zenisek, Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations. Academic Press, London (1990). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you