Analysis of a one-dimensional nonlocal quasi-continuum method. (English) Zbl 1177.74169

Ming, Pingbing; Yang, Jerry Zhijian

Multiscale Model. Simul. 7, No. 4, 1838-1875 (2009).

Summary: The accuracy of the quasi-continuum method is analyzed using a series of models with increasing complexity. It is demonstrated that the existence of the ghost force may lead to large errors. It is also shown that the ghost force removal strategy proposed by E, Lu, and Yang leads to a version of the quasi-continuum method with uniform accuracy.

MSC:

74G20	Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
74G15	Numerical approximation of solutions of equilibrium problems in solid mechanics
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N06	Finite difference methods for boundary value problems involving PDEs

Keywords:

quasi-continuum method; ghost force; geometrically consistent scheme