Year: 2023
Author: Dan Li, Yiqiang Li, Zhanbin Yuan
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 5 : pp. 647–666
Abstract
A new weak Galerkin method with weakly enforced Dirichlet boundary condition is proposed and analyzed for the second order elliptic problems. Two penalty terms are incorporated into the weak Galerkin method to enforce the boundary condition in the weak sense. The new numerical scheme is designed by using the locally constructed weak gradient. Optimal order error estimates are established for the numerical approximation in the energy norm and usual $L^2$ norm. Moreover, by using the Schur complement technique, the unknowns of the numerical scheme are only defined on the boundary of each piecewise element and an effective implementation of the reduced global system is presented. Some numerical experiments are reported to demonstrate the accuracy and efficiency of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1028
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 5 : pp. 647–666
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: weak Galerkin finite element methods weak gradient second order elliptic problems polytopal partitions.