Robust Finite Element Schemes for Inhomogeneous Bi-Laplace Problems

This paper presents lowest-degree robust finite element schemes for solving inhomogeneous bi-Laplace problems, including an inhomogeneous fourth-order elliptic singular perturbation problem and a Helmholtz transmission eigenvalue problem. The schemes use the reduced rectangle Morley (RRM) element space with piecewise quadratic polynomials, which are of the lowest degree possible.