Emmrich, Etienne2018-10-102018-10-1020071609-4840https://depositonce.tu-berlin.de/handle/11303/8310http://dx.doi.org/10.14279/depositonce-7461The third-kind boundary-value problem for a second-order elliptic equation on a polygonal domain with variable coefficients, mixed derivatives, and first-order terms is approximated by a linear finite element method with first-order accurate quadrature. The corresponding bilinear form does not need to be strongly positive. The discretisation is equivalent to a finite difference scheme. Although the discretisation is in general only first-order consistent, supraconvergence, i.e., convergence of higher order, is shown to take place even on nonuniform grids. If neither oblique boundary sections nor mixed derivatives occur, then the optimal order s is achieved. The supraconvergence result is equivalent to the supercloseness of the gradient.en510 Mathematikelliptic PDEfully discrete FEMnonuniform gridsupraconvergencesupercloseness of gradientArticle1609-9389