A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition

Shenglan Xie; Maoan Han; Peng Zhu

doi:10.3934/dcdsb.2020340

Article Contents

2021, Volume 26, Issue 10: 5217-5226. Doi: 10.3934/dcdsb.2020340

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A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition

1.
Nanhu College, Jiaxing University, Jiaxing, 314001, China
2.
Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China, Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
3.
College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, 314001, China

^* Corresponding author: P. Zhu
^* Corresponding author: P. Zhu

Received: August 31, 2018

Revised: August 31, 2019

Early access: November 2020

Published: October 2021

P. Zhu is supported by Zhejiang Provincial Natural Science Foundation of China (Grant No.LY19A010008)

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Abstract

A reliable and efficient a posteriori error estimator is presented for a weak Galerkin finite element method without stabilizer for the second order elliptic equation with mixed boundary conditions. The upper bound of the estimator is proved by Helmholtz decomposition technique and lower bound is hold naturally. The performance of the estimator is illustrated by numerical experiments.

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Mathematics Subject Classification: Primary: 65N15, 65N30.

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Figure 1. Initial mesh for adaptive refinement

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Figure 2. Effectivity index for Example 1

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Figure 3. Example 1. Final adaptive refinement mesh and WG solution

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Figure 4. Effectivity index for Example 2

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Figure 5. Example 2. Final adaptive refinement mesh and WG solution

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Figure 6. Effectivity index for Example 3

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Figure 7. Example 3. Final adaptive refinement mesh and WG solution

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