An immersed finite element method for elliptic interface problems on surfaces

In this article, an immersed finite element approach is presented for solving interface problems of elliptic PDEs on curved surfaces. Such surface PDEs involve discontinuities in the coefficients. The immersed surface finite element method can avoid complicated body-fitting surface grids generating. The construction of immersed surface finite element space uses generic linear basis functions over non-interface components while the piecewise linear basis functions satisfying jump conditions are applied on interface elements. Thus the proposed approach can efficiently capture the sharp solutions across the interface, and performs substantially superior to the conventional surface finite element method. The error estimate of energy norm is shown. Numerical examples verify the superiorities of the presented method.