The local ultraconvergence of high-order finite element method for second-order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high-degree finite element method based on a rectangular partition for the second-degree elliptic problem with constant coefficients Lu equivalent to- partial differential partial differential yi mml:mfenced close=")" open="(" separators=""aij partial differential u partial differential yj=fmml:mfenced close=")" open="(" separators=""y in omega subset of R-2, u(y) = 0 on partial differential omega. Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k >= 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.