In this paper, we propose a robust framework based on the scaled boundary finite element
method to model implicit interfaces in two-dimensional differential equations in
nonhomegeneous media. The salient features of the proposed work are:(a) interfaces can
be implicitly defined and need not conform to the background mesh;(b) Dirichlet boundary
conditions can be imposed directly along the interface;(c) does not require special numerical
integration technique to compute the bilinear and the linear forms and (d) can work with an …