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Numerical Algorithms

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18-11-2021 | Original Paper

Convergence of an adaptive modified WG method for second-order elliptic problem

Authors: Yingying Xie, Liuqiang Zhong, Yuping Zeng

Published in: Numerical Algorithms | Issue 2/2022

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Abstract

In this paper, an adaptive modified weak Galerkin (AMWG) method is considered to solve second-order elliptic problem. Under the assumption of a penalty parameter, by showing reliability of error estimator, comparison of solutions and reduction of error estimator, the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops, is proved to be a contraction, namely, the adaptive algorithm is convergent. Numerical experiments are implemented to support the theoretical results.

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Title: Convergence of an adaptive modified WG method for second-order elliptic problem
Authors: Yingying Xie
Liuqiang Zhong
Yuping Zeng
Publication date: 18-11-2021
Publisher: Springer US
Published in: Numerical Algorithms / Issue 2/2022
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-021-01209-3

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