Local integral equations in non-homogeneous media

A new approach based on the domain element approximation and local integral equations (LIE) is applied to solution of two-dimensional potential problems in materials with an arbitrary continuous variation of material coefficients. Quadratic serendipity domain elements are employed for approximation of the potential field as well as the geometry like in finite element method. The local integral equations are considered on sub-domains and collocated at interior nodes. Several numerical examples are considered in the convergence study with respect to the element size.