This article concerns the construction of a posteriori error estimates for the boundary element methods in plate-bending problems. The proposed approach allows one to assess the size of the error of a numerical solution through an accurate satisfaction of the prescribed boundary conditions. This error estimate analysis can also be used for boundary-type method formulations such as the Trefftz method, the boundary collocation method, and so on.
Get full access to this article
View all access options for this article.
References
1.
[1] Miranda, C.: Partial Differential Equations of Elliptic Type, Springer-Verlag, New York, 1970.
2.
[2] Fichera, G.: Ii Teorema del massimo modulo per 1'equazione dell'Elastostatica tridimensionale. Arch. Rational Mech. Anal., 7(5), 373-387 (1961).
3.
[3] Agmon, S: Maximum theorems for solution of higher order elliptic equations. Bull. Amer. Math. Soc., 66(2), 77-80 (1966).
4.
[4] Banerjee, P. K. and Butterfield, R.: Boundary Element Methods in Engineering Science, McGraw-Hill, London, 1981.
5.
[5] Brebbia, C. A., Telles, J.C.F., and Wrobel, L. C.: Boundary Element Techniques, Springer-Verlag, Berlin, 1984.
6.
[6] Kolodziej, J. A.: Review of application of boundary collocation method in mechanics of continuous media. Solid Mechanics Archives, 12, 187-231 (1987).
[8] Babuska, I.: A posteriori error estimation for the finite element method. Nonlinear Finite Element Analysis in Structural Mechanics: Proc. Europe-U.S. Workshop, 28-30 (1980).
9.
[9] Kelly, D. W., De, J. P., Gago, S. R., and Zienkiewicz, O. Z.: A posteriori error analysis and adaptive processes in the finite element method. Int. Journalfor Numer Methods in Engineering, 19, 1593-1619 (1983).
10.
[10] Rank, E.: A-posteriori error estimates and adaptive refinement for some boundary element methods, in Proc. Int. Conf on Accuracy Estimates and Adaptive Refinements in Finite Element Comp., ARFEC, Lisbon, 1984.
11.
[11] De-hao Yu: A-posteriori error estimates and adaptive approaches for some boundary element methods, Proc. of the Ninth International Conference on Boundary Element Methods, pp. 241-256, ed., C. A. Brebbia, W. L. Wendlund, and G. Kuhn, Computational Mechanics Publications, Southampton, UK, 1987.
12.
[12] Ventsel, E. S. and Eremenko, S. V.: Numerical solution of plate bending problems by the compensative load method, in Proc. of All-Union Conf on Integral Equations and Boundary Value Problems of Mathematical Physics, pp. 18-24, Vladivostok, Russia, 1990 (in Russian).
13.
[13] Mikhlin, S. G.: Variational Methods in Mathematical Physics, Macmillan, New York, 1964.
14.
[14] Adams, R. A.: Sobolev Spaces, Academic Press, New York, 1975.
15.
[15] Fichera, G.: Existence Theorems in Elasticity, Springer-Verlag, Berlin, 1972.
16.
[16] Birman, M. S.: Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory, American Mathematical Society, Providence, RI, 1980.
17.
[17] Varga, R.: Functional Analysis and Approximation Theory in Numerical Analysis, Society for Industrial and Applied Mathematics, Philadelphia, 1971.
18.
[18] Mikhlin, S. G.: Constants in Some Inequalities Analysis, John Wiley, New York, 1986.
19.
[19] Courant, R.: Methods of Mathematical Physics, Interscience Publishers, New York, 1962.