Anisotropic immersed finite element methods for 1D elliptic interface systems

Abstract In this article, we study anisotropic immersed finite element (AIFE) methods for the elliptic interface system. After establishing the existence and uniqueness of the weak solution, we construct a linear AIFE method for solving the interface system. Different from the scalar problem, the jump conditions for each unknown function are coupled together in the anisotropic problem considered here. Through defining suitable interpolations, we deduce the error estimates in and for the proposed AIFE method. Moreover, we show some numerical experiments to verify the correction of the theoretical predictions.