A-posteriori error estimate for the coupling of BEM and mixed-FEM

Numerical Functional Analysis and Optimization

Volumn 20, Issue 5-6, 1999, Pages 449-472

  Gatica, Gabriel N ^a   Meddahi, Salim ^b  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

^b UNIVERSITY OF OVIEDO   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; FINITE ELEMENT METHOD; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

A POSTERIORI ERROR ESTIMATE; SECOND ORDER ELLIPTIC EQUATION;

ERROR ANALYSIS;

EID: 0033154256     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569908816905     Document Type: Article

References (44)

1. D. ACHCHAB, A. AGOUZAL, J. BARANGER AND J.F. MAITRE, Estimateur d'erreur a posteriori hiérarchique. Application aux éléments finis mixtes, Numer. Math., 80 (1998), pp. 159-179.
2. R.A. ADAMS, Sobolev Space, Academic Press, New York, 1975.
3. A. ALONSO, Error estimator for a mixed method, Numerische Mathematik, 74 (1996), pp. 385-395.
4. M. AINSWORTH AND J.T. ODEN, A posteriori error estimation in finite element analysis, Comput. Methods. Appl. Mech. Engrg., 142 (1997), pp. 1-88.
5. K.J. ARROW, L. HURWICZ, AND H. UZAWA, Studies in Linear and Nonlinear Programming, Stanford University Press, 1958.
6. G.R. BARRENECHEA, G.N. GATICA AND J.-M. THOMAS, Primal mixed formulations for the coupling of FEM and BEM. Part I: linear problems, Numerical Functional Analysis and Optimization, 19 (1998), pp. 7-32.
7. D. BRAESS AND R. VERFÜRTH, A posteriori error estimators for the Raviart-Thomas element, SIAM J. Numer. Anal., 33 (1996), pp. 2431-2444.
8. J. BRAMBLE AND J. PASCIAK, A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comp., 50 (1988), pp. 1-17.
9. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer, Berlin Heidelberg New York, 1991.
10. 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), pp. 153-174.
11. C. CARSTENSEN, A posteriori error estimate for the symmetric coupling of finite elements and boundary elements, Computing, 57 (1996), pp. 301-322.
12. C. CARSTENSEN, An a posteriori error estimate for a first-kind integral equation, Math. Comp., 66 (1997), pp. 139-155.
13. C. CARSTENSEN, A-posteriori error estimate for the mixed finite element method, Math. Comp., 66 (1997), pp. 465-476.
14. C. CARSTENSEN, S.A. FUNKEN AND E.P. STEPHAN, A posteriori error estimates for hp-boundary element methods, Appl. Anal., 61 (1996), pp. 233-253.
15. 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), pp. 187-221.
16. C. CARSTENSEN AND E.P. STEPHAN, A posteriori error estimates for boundary element methods, Math. Comp., 64 (1995), pp. 483-500.
17. C. CARSTENSEN AND E.P. STEPHAN, Adaptive coupling of boundary elements and finite elements, Mathematical Modelling and Numerical Analysis, 29 (1995), pp. 779-817.
18. C. CARSTENSEN, E.P. STEPHAN AND D. ZARRABI, On the h-adaptive coupling of FE and BE for viscoplastic and elasto-plastic interface problems, J. Comput. Appl. Math., to appear
19. Z. CEN Q. DU, Some further works on the combination of hybrid/mixed finite elements to boundary elements, in Theory and Applications of Boundary Element Methods, edited by M. Tanaka et al., 1988, pp. 5-14, Pergamon Press, Oxford.
20. P. CLÉMENT, Approximation by finite element functions using local regularisation, R.A.I.R.O. Anal. Numer., 9 (1975), pp. 77-84.
21. M. COSTABEL, Symmetric methods for the coupling of finite elements and boundary elements, in Boundary Elements IX, vol. 1, edited by C.A. Brebbia et al., 1987, pp. 411-420, Springer-Verlag, Berlin.
22. M. COSTABEL, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal., 19 (1988), pp. 613-621.
23. R. EWING AND J. WANG, Analysis of the Schwarz algorithm for mixed finite element methods, R.A.I.R.O., Modél. Math. Anal. Numér., 26 (1992), pp. 739-756.
24. M. FEISTAUER, G.C. HSIAO AND R.E. KLEINMAN, Asymptotic and a posteriori error estimates for boundary element solutions of hypersingular integral equations, SIAM J. Numer. Anal., 33 (1996), pp 666-685.
25. G.N. GATICA, Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity, Applied Mathematics Letters, 10 (1997), pp. 29-35.
26. G.N. GATICA AND G.C. HSIAO, Boundary-Field Equation Methods for a Class of Nonlinear Problems, Pitman Research Notes in Mathematics Series, vol. 331, Longman, 1995.
27. G.N. GATICA AND W.L. WENDLAND, Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems, Applicable Analysis, 63 (1996), pp. 39-75.
28. G.N. GATICA AND W.L. WENDLAND, Coupling of mixed finite elements and boundary elements for a hyperelastic interface problem, SIAM Journal on Numerical Analysis, 34 (1997), pp. 2335-2356.
29. V. GIRAULT AND P.A. RAVIART, Finite Element Approximation of the Navier-Stokes Equations: Theory and Algorithms, Springer, Berlin Heidelberg New York, 1986.
30. R. GLOWINSKI AND M.F. WHEELER, Domain decomposition and mixed finite element methods for elliptic problems, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R., Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., Philadelphia, 1988, SIAM.
31. J.J. GRANNELL, On simplified hybrid methods for coupling of finite elements and boundary elements, in Boundary Elements IX, vol. 1, Edited by C.A. Brebbia et al., 1987, pp. 447-460, Springer-Verlag, Berlin.
32. P. GRISVARD, Elliptic, Problems in Nonsmooth, Domains, Pitman, 1985.
33. H. HAN, A new class of variational formulations for the coupling of finite and boundary element methods, J. Comput. Math., 8 (1990), pp. 223-232.
34. T.P. MATHEW, Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, Numer. Math., 65 (1993), pp. 469-492.
35. S. MEDDAHI, An optimal iterative process for the Johnson-Nedelec method of coupling boundary and finite elements, SIAM J. Numer. Anal., 35 (1998), pp. 1393-1415.
36. S. MEDDAHI, J. VALDÉS, O. MENÉNDEZ, AND P. PÉREZ, On the coupling of boundary integral and mixed finite element methods, Journal of Computational and Applied Mathematics, 69 (1996), pp. 113-124.
37. C. POLIZZOTTO AND M. ZITO, Variational formulations for coupled BE/FE methods in elastostatics, Zeitschrift fur Angewandte Mathematik und Mechanics, 74 (1994), pp. 533-543.
38. P.A. RAVIART AND J.-M. THOMAS, A mixed finite element, method for 2nd order elliptic problems, in Lecture Notes of Mathematics, B. E. A. Dold, ed., vol. 606, Springer, Berlin Heidelberg New York, 1975.
39. J.E. ROBERTS AND J.-M. THOMAS, Mixed and Hybrid Methods, in Handbook of Numerical Analysis, edited by P.G. Ciarlet and J.L. Lions, vol. II, Finite Element Methods (Part 1), 1991, North-Holland, Amsterdam.
40. D. SILVESTER AND A. WATHEN, Fast iterative solutions of stabilized stokes systems Part II: Using general block preconditioners, SIAM J. Numer. Anal., 31 (1994), pp. 1352-1367.
41. R. VERFÜRTH, A posteriori error estimators for the Stokes problem, Numer. Math., 55 (1989), pp. 309-325.
42. R. VERFÜRTH, A Review of A-Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, John Wiley and Teubner Series, Advances in Numerical Mathematics, 1996.
43. W.L. WENDLAND AND D. YU, Adaptive boundary element methods for strongly elliptic integral equations, Numer. Math., 53 (1988), pp. 539-558.
44. W.L. WENDLAND AND D. YU, A-posteriori local error estimates of boundary element methods with some pseudo-differential equations on closed curves, J. Comp. Math., 10 (1992), pp. 273-289.