Piecewise smooth approximation for elliptic systems solutions

The paper is devoted to the problem of piecewise smooth approximation for elliptic system solutions defined on triangular grids. It is shown that when we approximate a differential of such a solution by the differential of the approximating mapping the error depends on the triangles shapes and sizes. A mapping is build to approximate the differential with the error that does not depend on triangles in the grid. The analogous results are obtained for Beltrami equation solutions.