Error estimates for rotated \(Q_1^{rot}\) element approximation of the eigenvalue problem on anisotropic meshes (Q1023088)

The main object of this work is to study the approximate behavior of the nonconforming rotated \(Q_1^{rot}\) element for the second-order elliptic eigenvalue problem on anisotropic meshes. A special technique is employed to construct a function possessing the anisotropic property in rotated \(Q_1^{rot}\) space, which leads to the optimal errors of energy norm and \(L^{2}\) norm for the second-order elliptic boundary problem. The above results are then applied to the error analysis of eigenpairs and the associated optimal errors are derived. Numerical results are provided to show the validity of the theoretical analysis.