Error Estimation for Boundary Element Analysis
Publication: Journal of Engineering Mechanics
Volume 115, Issue 9
Abstract
An a posteriori error estimator is developed for boundary element solution of two‐dimensional and axisymmetric potential problems. Two local (element) error norms are formulated for potential and flux which exist in each element. The error norm evaluated for an element is the one for the unknown quantity. The global error norm is found by summing the local error norms. The evaluation of the local error norms for the potential aid flux is based on a projection process of adjacent boundary element solutions. The accuracy and reliability of the proposed error estimator is demonstrated by five problems.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alarcón, E., and Reverter, A. (1986). “p‐adaptive boundary elements.” Int. J. Num. Meth. Engrg., 23, 801–829.
2.
Alarcón, E., Reverter, A., and Molina, J. (1985). “Hierarchical boundary elements.” Comp. Struct. 20, 151–156.
3.
Atluri, S. N., Belytschko, T., Oden, J. T., and Reddy, J. N. (1986). “Adaptive methods.” Comp. Meth. Appl. Mech. Engrg., 55, 1–197.
4.
Babuska, I., Chandra, J., and Flaherty, J. (1983). Adaptive methods for partial differential equations, Proc. Workshop held at Univ. of Maryland, College Park, Md.
5.
Babuska, I., and Szabó, B. A. (1987). Finite element methods: I. Conceptual and theoretical foundations. Springer‐Verlag, New York, N.Y.
6.
Babuska, I., Zienkiewicz, O. C., Gago, J., and Oliveira, E. R. de A. (1986). Accuracy estimates and adaptive refinements in finite element computations. John Wiley and Sons, Inc., New York, N.Y.
7.
Bakr, A. A. (1986). The boundary integral equation method in axisymmetric stress analysis problems. Springer‐Verlag, Berlin, West Germany.
8.
Banerjee, P. K., and Butterfield, R. (1981). Boundary element methods in engineering science. McGraw‐Hill Book Co., Inc., London, England.
9.
Brebbia, C. A., Telles, J. C., and Wrobel, L. C. (1984). Boundary element techniques—Theory and applications in engineering, Springer‐Verlag, Berlin, West Germany, 81.
10.
Carey, G. F., and Kennon, S. (1987). “Adaptive mesh redistribution for a boundary (panel) method.” Int. J. Num. Meth. Engrg., 24, 2315–2325.
11.
Carey, G. F., and Oden, J. T. (1984). Finite element computational aspects, Vol. III. Prentice‐Hall, Inc., Englewood Cliffs, N.J., 23–129.
12.
Chapman, A. J. (1984), Heat transfer. Macmillan Publishing Co., New York, N.Y., 169.
13.
Crase, T. A. (1987). Advanced boundary element methods. Springer‐Verlag, Berlin, West Germany.
14.
FIESTA: Theoretical Literature. (1984). Inst. Sperimentale Mod. Strut. (ISMES), Bergamo, Italy.
15.
Gallagher, R. H. (1987). “Thirty years of finite element analysis—Are there issues yet to be resolved?” Proc. 1987 ANSYS Conf., D. E. Dietrich, M. P. Powers, and J. I. Finkel, eds. Newport Beach, Calif.
16.
Ghia, K., and Ghia, U. (1983). Advances in grid generation. (ASME Mono. FED‐5), Amer. Soc. of Mech. Engrs., New York, N.Y.
17.
Hinton, E., and Campbell, J. S. (1974). “Local and global smoothing of discontinuous finite element functions using a least squares method.” Int. J. Num. Meth. Engrg., 8, 461–480.
18.
Ingber, M. S., and Mitra, A. K. (1986). “Grid optimization for the boundary element method.” Int. J. Num. Meth. Engrg. 23, 2121–2136.
19.
Kelly, D. W., Mills, R. J., Reizes, J. A., and Miller, A. D. (1987). “A posteriori estimates of the solution caused by discretization in the finite element, finite difference and boundary element methods.” Int. J. Num. Meth. Engrg. 24, 1921–1939.
20.
Mullen, R. L., and Rencis, J. J. (1987). “Iterative methods for solving boundary element equations.” Comp. Struct. 25(5), 713–723.
21.
Mukherjee, S. (1982). Boundary element methods in creep and fracture. Appl. Sci. Publishers, London, England.
22.
Rank, E. (1986). “Adaptivity and accuracy estimation for finite element and boundary integral element methods.” Accuracy estimates and adaptive refinements in finite element computations, I. Babuska, O. C. Zienkiewicz, J. Gago, E. R. de A. Oliveira, eds. John Wiley and Sons, Chichester, England.
23.
Rencis, J. J., and Jong, K. Y. (1988). “An accuracy postprocessor for boundary element analysis.” BE 10, C. A. Brebbia, ed. Computat. Mech. Publications, Southampton, England.
24.
Rencis, J. J., and Mullen, R. L. (1986). “Solution of elasticity problems by a self adaptive mesh refinement technique for boundary element computation.” Int. J. Num. Meth. Engrg., 23, 1509–1527.
25.
Rencis, J. J., and Mullen, R. L. (1988a). “A gepmetric preprocessor for an h‐refinement technique for the boundary element method.” Advanced boundary element method, T. A. Cruse, ed. Springer‐Verlag, Berlin, West Germany.
26.
Rencis, J. J., and Mullen, R. L. (1988b). “A self adaptive mesh refinement technique for the boundary element solution of the Laplace equation.” Comp. Mech., 3, 309–319.
27.
Shephard, M., and Gallagher, R. (1979). Finite element grid optimization. (ASME Mono. PVP‐38), Amer. Soc. of Mech. Engrs., New York, N.Y.
28.
Szabó, B. A. (1986). PROBE: Theoretical manual. NOETIC Tech. Corp., 7980 Clayton Road, Suite 205, St. Louis, Mo.
29.
Telles, J. C. F. (1983). The boundary element method applied to inelastic problems. Springer‐Verlag, Berlin, West Germany.
30.
Yoshikawa, F., and Tanaka, M. (1982). “Boundary elements in axisymmetric potential problems.” Boundary elements methods in engineering, C. A. Brebbia, ed. Springer‐Verlag, Berlin, West Germany.
31.
Zienkiewicz, O. C., and Zhu, J. Z. (1987). “A simple error estimator and adaptive procedure for practical engineering analysis.” Int. J. Num. Meth. Engrg., 24, 337–357.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Sep 1, 1989
Published in print: Sep 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.