We present a mesh adaptation method by node movement for two-dimensional linear elasticity problems with unilateral contact. The adaptation is based on a hierarchical estimator on finite element edges and the node displacement techniques use an analogy of the mesh topology with a spring network. We show, through numerical examples, the efficiency of the present adaptation method.
@article{bwmeta1.element.bwnjournal-article-amcv12i1p9bwm, author = {B\'eal, Pierre and Koko, Jonas and Touzani, Rachid}, title = {Mesh r-adaptation for unilateral contact problems}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {12}, year = {2002}, pages = {9-16}, zbl = {1038.74040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv12i1p9bwm} }
Béal, Pierre; Koko, Jonas; Touzani, Rachid. Mesh r-adaptation for unilateral contact problems. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) pp. 9-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv12i1p9bwm/
[000] D'azevedo E.F. (1991): Optimal triangular mesh generation by coordinate transformation. - SIAM J. Sci. Stat. Comput., Vol. 12, No. 4, pp. 755-786. | Zbl 0736.65001
[001] D'azevedo E.F. and Simpson R.B. (1991): On optimal triangular meshes for minimizing the gradient error. - Num. Math., Vol. 59, No. 4, pp. 321-348. | Zbl 0724.65006
[002] Fortin M. (1998): Anisotropic mesh adaptation through hierarchical error estimators. - SIAM J. Numer. Anal., Vol. 26, No. 4, pp. 788-811.
[003] Habashi W.G., Fortin M., Yahia D.A.A., Boivin S., Bourgault Y., Dompierre J., Robichaud M.P., Tam A. and Vallet M.-G. (1996): Anisotropic Mesh Optimization. Towards a Solver-Independent and Mesh-Independent CFD. - Lecture Series in Computational Fluid Dynamics, Von Karman Institute for Fluid Dynamics.
[004] Haslinger J., Neitaanmaki P. and Salmenjoki K. (1992): On FE-grid relocation in solving unilateral boundary value problems by fem. - Applics. Math., Vol. 37, No. 2, pp. 105-122. | Zbl 0757.65114
[005] Kikuchi N. and Oden J. (1988): Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. - Philadelphia, PA: SIAM. | Zbl 0685.73002
[006] Peraire J., Perió J. and Morgan K. (1992): Adaptive remeshing for three-dimensional compressible flow computation. - J. Comp. Phys., Vol. 103, No. 2, pp.269-285. | Zbl 0764.76037
[007] Tourigny Y. and Hulsemann F. (1998): A new moving mesh algorithm for the finite element solution of variational problems. - SIAM J. Numer. Anal., Vol. 35, No. 4, pp. 1416-1438. | Zbl 0913.65059