Immersed Finite Element Methods

We construct high-order finite element spaces and methods for interface problems modeled by partial differential equations with discontinuous coefficients. We propose several immersed finite element methods that allow elements to be cut by the interface and, thus, they contain more than one material. The proposed piecewise polynomial spaces partially solve the problem on interface elements. Applications include, but not limited to, the standard diffusion interface problems, flow interface problems and wave propagation and scattering interface problems.