Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: Weak Galerkin Method

Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: Weak Galerkin Method

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.

Author Details

Xiu Ye

Shangyou Zhang