Immersed finite element methods for 4th order differential equations

We propose three new finite element methods for solving boundary value problems of 4th order differential equations with discontinuous coefficients. Typical differential equations modeling the small transverse displacement of a beam and a thin plate formed by multiple uniform materials are considered. One important feature of these finite element methods is that their meshes can be independent of the interface between different materials. Finite element spaces based on both the conforming and mixed formulations are presented. Numerical examples are given to illustrate capabilities of these methods.