Zienkiewicz-Zhu's derivative patch recovery technique is analyzed for general quadri-lateral nite elements. Under certain regular conditions on the meshes, the arithmetic mean of the absolute error of the recovered gradient at the nodal points is superconver-gent for the second-order elliptic operators. For rectangular meshes and the Laplacian, the recovered gradient is superconvergent in the m...

Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems play an important role in mathematics and have many applications in natural sciences (see, for example, [1 – 6]). In 1988, the inverse nodal problem was posed and solved for Sturm-Liouville problems by J. R. McLaughlin [7], who showed that the knowledge of a dense subset of nodal points ...