Abstract. We construct and analyze discontinuous spline interpolation for the approximation of discontinuous functions. We develop an algorithm to estimate a discontinuous function whose unknown discontinuities lie on lines parallel to the coordinate axes, by approximating it by the discontinuous spline interpolation. We also develop an algorithm to find the discontinuities of a discontinuous function on the basis of the concept of ε-continuity of functions of two variables and present the examples.

Keywords: discontinuous function, discontinuous interpolating splines of two variables, discontinuous approximation, rectangular elements.