|
Organizers |
An adaptive two-level boundary element method for Signorini problems.
by
Matthias Maischak
Institute for Applied Mathematics, University of Hannover, Germany
We consider elliptic pde's (Laplace and Lamé) with Signorini-type boundary or transmission conditions. These problems can be rewritten in terms of variational inequalities with a symmetric and positive definite bilinear form involving the discretized Poincaré-Steklov operator, i.e. we use bem [2, 5] and fem-bem coupling formulations [1].
For these formulations we derive a posteriori estimates by using hierarchical basis techniques. Based on the properties of two-level additive Schwarz operators for hypersingular and weakly singular integral equations, easily computable local error indicators are obtained. An algorithm for adaptive error control which allows independent refinements of finite elements and boundary elements on the various grids involved is formulated and numerical results are given (cf. [3, 4]).
[1] C. Carstensen and J. Gwinner, FEM and BEM coupling for a nonlinear transmission problem with Signorini contact, SIAM J. Numer. Anal., 34 (1997), pp. 1845-1864.
[2] J. Gwinner and E. P. Stephan, A boundary element procedure for contact problems in linear elastostatics, RAIRO Math.Mod.Num.Anal., 27 (1993), pp. 457-480.
[3] M. Maischak, P. Mund, and E. P. Stephan, Adaptive multilevel bem for acoustic scattering, Comput.Methods Appl.Mech.Engrg., 150 (1997), pp. 351-367.
[4] P. Mund and E. P. Stephan, An adaptive two-level method for the coupling of nonlinear fem-bem equations, SIAM J.Numer.Analysis, 36 (1999), pp. 1001-1021.
[5] W. Spann, On the boundary element method for the Signorini problem of the Laplacian, Numer. Math., 65 (1993), pp. 337-356.
Date received: July 30, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-89.