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.W...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 in-teractions.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.展开更多
基金supported by National Natural Science Foundation of China grant 11861131004,11771040,91430106supported by Natural Science Foundation of China grant 11871339,11861131004,11571314,11471214 and the One Thousand Plan of China for young scientists.
文摘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 in-teractions.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.
