A flexible local approximation method for electro- and magnetostatics

A new framework for constructing variational-difference schemes with arbitrary local approximating functions is proposed. The key concept is multivalued approximation on a system of overlapping "patches," with continuity of the solution imposed only at grid nodes. In particular, curved material interfaces can be represented on regular geometrically nonconforming grids by special local approximating functions. Problems with spherical particles are considered as an example.