We consider a standard Adaptive weak Galerkin (AWG) finite element method for second order elliptic problems. We prove that the sum of the energy error and the scaled error estimator of AWG method, between two consecutive adaptive loops, is a contraction. At last, we present some numerical experiments to support the theoretical results.

中文翻译：

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二阶椭圆问题的自适应弱Galerkin有限元方法的收敛性

我们考虑用于二阶椭圆问题的标准自适应弱Galerkin（AWG）有限元方法。我们证明了两个连续的自适应回路之间的能量误差和AWG方法的比例误差估计量之和是一个收缩。最后，我们提出了一些数值实验来支持理论结果。