Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes

Abstract EN

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.