A posteriori boundary element error estimation

Journal of Computational and Applied Mathematics

Volumn 106, Issue 1, 1999, Pages 1-19

  Jou, Jang ^a   Liu, Jinn Liang ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

A posteriori error estimate; Adaptive computation; Boundary element method; Boundary integral equation

Indexed keywords

ERROR ANALYSIS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

ADAPTIVE COMPUTATION; BOUNDARY INTEGRAL EQUATIONS;

BOUNDARY ELEMENT METHOD;

EID: 0032636663     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00049-7     Document Type: Article

References (27)

1. S. Adjerid, J.E. Flaherty, Second-order finite element approximations and a posteriori error estimation for two-dimensional parabolic systems, Numer. Math. 53 (1988) 183-198.
2. S. Adjerid, J.E. Flaherty, Y.J. Wang, A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems, Numer. Math. 65 (1993) 1-21.
3. R.E. Bank, Hierarchical bases and the finite element method, Acta Numerica 1996 (A. Iserles, ed.), Cambridge University Press (1996) 1-43.
4. R.E. Bank, R.K. Smith, A posteriori error estimates based on hierarchical bases, SIAM J. Numer. Anal. 30 (1993) 921-935.
5. T. Cao, Adaptive H-and H-R methods for symm's integral equation, Comput. Methods Appl. Mech. Eng. 162 (1998) 1-17.
6. C. Carstensen, An a posteriori error estimate for a first-kind integral equation, Math. Comp. 66 (1997) 139-155.
7. C. Carstensen, D. Estep, P. Stephan, h-adaptive boundary element schemes, Comput. Mech. 15 (1995) 372-383.
8. C. Carstensen, E.P. Stephan, A posteriori error estimates for boundary element methods, Math. Comp. 64 (1995) 483-500.
9. G. Chen, J. Zhou, Boundary Element Methods, Academic Press, San Diego, CA, 1992.
10. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, New York, 1978.
11. M. Costabel, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988) 613-626.
12. V. Eijkhout, P. Vassilevski, The role of the strengthened Cauchy-Buniakowskii-Schwarz inequality in multilevel methods, SIAM Rev. 33 (1991) 405-419.
13. M. Feistauer, G.C. Hsiao, R.E. Kleinman, Asymptotic and a posteriori error estimates for boundary element solution of hypersingular integral equations, SIAM J. Numer. Anal. 33 (1996) 666-687.
14. 2, Numer. Math. 61 (1992) 171-214.
15. N. Heuer, E.P. Stephan, T. Tran, Multilevel adaptive Schwarz method for the h-p version of the Galerkin boundary element method, Math. Comp. 67 (1998) 501-518.
16. G.C. Hsiao, S. Zhang, Optimal order multigrid methods for solving exterior boundary value problems, SIAM J. Numer. Anal. 31 (1994) 680-694.
17. J.L. Lions, E. Magenes, Non-Homogeneous Elliptic Boundary Value Problems and Applications, vol. I, Springer, Berlin, 1972.
18. J.-L. Liu, Weak residual error estimates for symmetric positive systems, Numer. Funct. Anal. Optim. 14 (1993) 607-619.
19. J.-L. Liu, On weak residual error estimation, SIAM J. Sci. Comput. 14 (1996) 1249-1268.
20. J.-L. Liu, I.-J. Lin, M.-Z. Shih, R.-C. Chen, M.-C. Hsieh, Object oriented programming of adaptive finite element and finite volume methods, Appl. Numer. Math. 21 (1996) 439-467.
21. J.-L. Liu, W.C. Rheinboldt, A posteriori finite element error estimators for indefinite elliptic boundary value problems, Numer. Funct. Anal. Optim. 15 (1994) 335-356.
22. J.-L. Liu, W.C. Rheinboldt, A posteriori finite element error estimators for parametrized nonlinear boundary value problems, Numer. Funct. Anal. Optim. 17 (1996) 605-637.
23. F.V. Postell, P. Stephan, On the h-, p-and h-adaptive versions of the boundary element method-numerical results, Comput. Methods Appl. Mech. Eng. 83 (1990) 69-89.
24. I.H. Sloan, A. Spence, The Galerkin method for integral equations of the first kind with logarithmic kernel: Theory, IMA J. Numer. Anal. 8 (1988) 105-122.
25. W.L. Wendland, P. Stephan, A hypersingular boundary integral method for two-dimensional screen and crack problems, Arch. Rational Mech. Anal. 112 (1990) 363-390.
26. W.L. Wendland, D. Yu, Adaptive boundary element methods for strongly elliptic integral equations, Numer. Math. 53 (1988) 539-558.
27. W.L. Wendland, D. Yu, A posteriori local error estimates of boundary element methods with some pseudo-differential equations on closed curves, J. Comput. Math. 10 (1992) 273-289.