The convergence analysis of a Morley type rectangular element for the fourth-order elliptic singular perturbation problem is considered. A counterexample is provided to show that the element is not uniformly convergent with respect to the perturbation parameter. A modified finite element approximation scheme is used to get convergent results; the corresponding error estimate is presented under anisotropic meshes. Numerical experiments are also carried out to demonstrate the theoretical analysis.
"Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/234375