Year: 2022
Author: Xiu Ye, Shangyou Zhang
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 3 : pp. 590–598
Abstract
A simple stabilizer free weak Galerkin (SFWG) finite element method for a one-dimensional second order elliptic problem is introduced. In this method, the weak function is formed by a discontinuous $k$-th order polynomial with additional unknowns defined on vertex points, whereas its weak derivative is approximated by a polynomial of degree $k+1.$ The superconvergence of order two for the SFWG finite element solution is established. It is shown that the elementwise lifted $P_{k+2}$ solution of the $P_k$ SFWG one converges at the optimal order. Numerical results confirm the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.030921.141121
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 3 : pp. 590–598
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Finite element weak Galerkin stabilizer free.