Abstract
This paper presents a posteriori error estimate for the weak Galerkin (WG) finite element method used to solve H(curl)-elliptic problems. Firstly, we introduce a WG method for solving H(curl)-elliptic problems and a corresponding residual type error estimator without a stabilization term. Secondly, we establish the reliability of the error estimator by demonstrating that the stabilization term is controlled by the error estimator. We also evaluate the efficiency of the error estimator using standard bubble functions. Finally, we present some numerical results to show the performances of the error estimator in both uniform and adaptive meshes.
Funding statement: Funding: The authors are supported by the National Natural Science Foundation of China (No. 12071160); The first author is also supported by the National Natural Science Foundation of China (No. 12101250) and the Science and Technology Projects in Guangzhou (No. 202201010644); The second author is supported by the National Natural Science Foundation of China (No.12101147).
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