On the application of the Arlequin method to the coupling of particle and continuum models

@article{citeulike:3042461, abstract = {Abstract\ \ In this work, we propose to extend the Arlequin framework to couple particle and continuum models. Three different coupling strategies are investigated based on the L 2 norm, H 1 seminorm, and H 1 norm. The mathematical properties of the method are studied for a one-dimensional model of harmonic springs, with varying coefficients, coupled with a linear elastic bar, whose modulus is determined by simple homogenization. It is shown that the method is well-posed for the H 1 seminorm and H 1 norm coupling terms, for both the continuous and discrete formulations. In the case of L 2 coupling, it cannot be shown that the Babu\v{s}ka–Brezzi condition holds for the continuous formulation. Numerical examples are presented for the model problem that illustrate the approximation properties of the different coupling terms and the effect of mesh size.}, author = {Bauman, Paul and Dhia, Hachmi and Elkhodja, Nadia and Oden, J. and Prudhomme, Serge }, citeulike-article-id = {3042461}, doi = {10.1007/s00466-008-0291-1}, journal = {Computational Mechanics}, keywords = {mathematics, mechanics, multiscale}, number = {4}, pages = {511--530}, posted-at = {2008-07-25 12:06:05}, priority = {0}, title = {On the application of the Arlequin method to the coupling of particle and continuum models}, url = {http://dx.doi.org/10.1007/s00466-008-0291-1}, volume = {42}, year = {2008} }

TY - JOUR ID - citeulike:3042461 L3 - citeulike-article-id:3042461 TI - On the application of the Arlequin method to the coupling of particle and continuum models JF - Computational Mechanics VL - 42 IS - 4 SP - 511 EP - 530 N2 - Abstract  In this work, we propose to extend the Arlequin framework to couple particle and continuum models. Three different coupling strategies are investigated based on the L 2 norm, H 1 seminorm, and H 1 norm. The mathematical properties of the method are studied for a one-dimensional model of harmonic springs, with varying coefficients, coupled with a linear elastic bar, whose modulus is determined by simple homogenization. It is shown that the method is well-posed for the H 1 seminorm and H 1 norm coupling terms, for both the continuous and discrete formulations. In the case of L 2 coupling, it cannot be shown that the Babuška–Brezzi condition holds for the continuous formulation. Numerical examples are presented for the model problem that illustrate the approximation properties of the different coupling terms and the effect of mesh size. KW - mathematics KW - mechanics KW - multiscale AU - Bauman, Paul AU - Dhia, Hachmi AU - Elkhodja, Nadia AU - Oden, J AU - Prudhomme, Serge PY - 2008//01/ UR - http://dx.doi.org/10.1007/s00466-008-0291-1 ER -