Discontinuous Galerkin immerse finite volume element method for elliptic interface problems

By choosing the trial function space to the immersed finite element space and the test function space to be piecewise constant function space, we develop a discontinuous Galerkin immersed finite volume element method to solve the elliptic interface problems. The existence and uniqueness of the discrete scheme is proved, and an optimal energy-norm error estimate and L²-norm estimate for the numerical solution are obtained.