Multiscale nonconforming finite element computation to small periodic composite materials of elastic structures on anisotropic meshes (Q1793535)

Summary: The small periodic elastic structures of composite materials with the multiscale asymptotic expansion and homogenized method are discussed. A nonconforming Crouzeix-Raviart finite element is applied to calculate every term of the asymptotic expansion on anisotropic meshes. The approximation scheme to the higher derivatives of the homogenized solution is also derived. Finally, the optimal error estimate in \(\| \cdot \|_h\) for displacement vector is obtained.