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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

Received  September 2018 Revised  September 2019 Published  November 2020

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

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.

Citation: Shenglan Xie, Maoan Han, Peng Zhu. A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020340
##### References:

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##### References:
Effectivity index for Example 1
Example 1. Final adaptive refinement mesh and WG solution
Effectivity index for Example 2
Example 2. Final adaptive refinement mesh and WG solution
Effectivity index for Example 3
Example 3. Final adaptive refinement mesh and WG solution
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