Toprakseven, Şuayip2021-12-232021-12-232022Toprakseven, S. (2022). Superconvergence of a modified weak Galerkin method for singularly perturbed two-point elliptic boundary-value problems. Calcolo, 59(1), 1-35.https://hdl.handle.net/11494/3617In this paper, superconvergence approximations of the modified weak Galerkin finite element method for the singularly perturbed two-point elliptic boundary-value problem have been studied. On the piecewise uniform Shishkin mesh, we have established the superconvergence error bounds of O(N-1 ln N)(k+1) in the discrete energy norm, where k is the degree of polynomials used in the finite element space and N is the number of elements. Stability analyses have been carried out for both singularly perturbed reaction-diffusion and convection-dominated problems. Some numerical examples are presented to support the theoretical findings. Moreover, the numerical experiments show that the proposed method has the superconvergence error bounds of O(N-1 ln N)(2k) in the discrete L-infinity-norm.eninfo:eu-repo/semantics/closedAccessArticle59110.1007/s10092-021-00449-yQ1Q1