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<p>In this article a residual based <i>a posteriori</i> error estimator is proposed for the Modified Weak Galerkin (MWG) finite element method applied to the obstacle problem. The estimator is proven to be both reliable and efficient in assessing the approximation error in a natural energy norm. The analysis hinges on the decomposition of the discrete solution into conforming and non-conforming components, which plays a crucial role in error estimation. Numerical experiments validate the theoretical results, demonstrating the accuracy and effectiveness of the proposed approach.</p>

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Adaptive Modified Weak Galerkin Method for Obstacle Problem

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Tanvi Wadhawan

摘要

In this article a residual based a posteriori error estimator is proposed for the Modified Weak Galerkin (MWG) finite element method applied to the obstacle problem. The estimator is proven to be both reliable and efficient in assessing the approximation error in a natural energy norm. The analysis hinges on the decomposition of the discrete solution into conforming and non-conforming components, which plays a crucial role in error estimation. Numerical experiments validate the theoretical results, demonstrating the accuracy and effectiveness of the proposed approach.