论文标题
关于混合拉普拉斯特征值问题的渐近确切的后验错误估计的注释
A note on asymptotically exact a posteriori error estimates for mixed Laplace eigenvalue problems
论文作者
论文摘要
我们得出了Laplace特征值问题的近似值的最佳和渐近的后验误差估计。为此，我们结合了文献的两个结果。首先，我们使用开发的Hyprcircle技术，用于与Raviart-Thomas有限元素的混合特征值近似。此外，我们还使用基于Brezizi-Douglas-Marini有限元的混合近似值为特征值和本本特征功能引入的后处理。为了结合这些方法，我们为适当修改差异的通量定义了一种新颖的局部后处理。因此，新通量可用于得出上限，并且仍然显示出良好的近似特性。数值示例验证了理论并激发了自适应网状细化的使用。
We derive optimal and asymptotically exact a posteriori error estimates for the approximation of the Laplace eigenvalue problem. To do so, we combine two results from the literature. First, we use the hypercircle techniques developed for mixed eigenvalue approximations with Raviart-Thomas Finite elements. In addition, we use the post-processings introduced for the eigenvalue and eigenfunction based on mixed approximations with the Brezzi-Douglas-Marini Finite element. To combine these approaches, we define a novel additional local post-processing for the fluxes that appropriately modifies the divergence. Consequently, the new flux can be used to derive upper bounds and still shows good approximation properties. Numerical examples validate the theory and motivate the use of an adaptive mesh refinement.
