论文标题
四元卷曲问题的galerkin有限元方法
Weak Galerkin Finite Element Methods for Quad-Curl Problems
论文作者
论文摘要
本文介绍了三个维度的四边形问题的薄弱的galerkin（WG）有限元方法。事实证明，所提出的WG方法在离散规范中的精确解决方案的最佳误差估算顺序中是稳定且准确的。此外，除最低订单$ k = 1，2 $是为WG解决方案衍生而来的$ L^2 $错误估算。进行了一些数值实验来验证我们的WG方法的效率和准确性，此外，从数值结果中也观察到了超浓缩。
This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG method is stable and accurate in an optimal order of error estimates for the exact solution in discrete norms. In addition, an $L^2$ error estimate in an optimal order except the lowest orders $k=1, 2$ is derived for the WG solution. Some numerical experiments are conducted to verify the efficiency and accuracy of our WG method and furthermore a superconvergence has been observed from the numerical results.
