论文标题
stokes特征值问题的混合不连续galerkin方法的后验错误估计
A posteriori error estimates of mixed discontinuous Galerkin method for the Stokes eigenvalue problem
论文作者
论文摘要
在本文中，对于$ d $ - 维情况中的特征值问题$（d = 2,3）$，我们提出了使用$ p_ {k} -p_ {k-1} $（k-1} $（k-1} $（k \ ege geq 1）$ p_ {k}的混合不连续的Galerkin有限元方法残余类型的后验错误估计。我们为近似本特征的后验误差估计量提供了估计值，证明了其本征函数的可靠性和效率，并分析了其特征值的可靠性。我们实施自适应计算，数值结果证实了我们的理论预测，并表明我们的方法可以实现最佳收敛顺序$ O（dof^{ - 2k/d}）$。
In this paper, for the Stokes eigenvalue problem in $d$-dimensional case $(d=2,3)$, we present an a posteriori error estimate of residual type of the mixed discontinuous Galerkin finite element method using $P_{k}-P_{k-1}$ element $(k\geq 1)$. We give the a posteriori error estimators for approximate eigenpairs, prove their reliability and efficiency for eigenfunctions, and also analyze their reliability for eigenvalues. We implement adaptive calculation, and the numerical results confirm our theoretical predictions and show that our method can achieve the optimal convergence order $O(dof^{-2k/d})$.
