UC Irvine

We developed a simplified formulation of the existing immersed finite element (IFE) methods for solving the second order elliptic interface problems. A virtual body-fitted mesh is generated using the intersection points of the interface and the underlying shape regular triangulation. We define an immersed virtual element local space. By deriving an error equation and performing convergence analysis base on it, we not only create a more concise formulation and convergence proof of partially penalized IFE method, but also brings a connection between various methods such as body-fitted FEM, IFEM, VEM, etc. In addition, our approach has the advantage that it is easier to generalize into three dimension case.