@Article{CiCP-27-198, author = {Liao , MingjieLin , Ping and Zhang , Lei}, title = {A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {1}, pages = {198--226}, abstract = {

In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is quasi-optimal if the continuum model is discretized by P1 finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0169}, url = {http://global-sci.org/intro/article_detail/cicp/13319.html} }