论文标题
节点辅助A后验错误估计值
Nodal auxiliary a posteriori error estimates
论文作者
论文摘要
我们介绍并解释了后验误差估计与子空间校正方法之间的关键关系，这些方法被视为无限尺寸希尔伯特空间中问题的预处理。我们使用有限元外观演算和节点辅助空间预处理设置舞台。该框架提供了一种系统的方法来基于本地问题的局部问题来得出明确的剩余估计器和估计量，这些问题是真正错误的上限和下限。我们将应用于$ΔD$，卷 - 卷曲，Grad-div，Hodge laplacian问题和弱对称性线性弹性的离散化应用。我们还为奇异扰动的H（D）规范和独立于参数的误差估计器提供了新的常规分解。唯一需要的成分是：问题的适合性和连续水平的常规分解。
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert spaces. We set the stage using the Finite Element Exterior Calculus and Nodal Auxiliary Space Preconditioning. This framework provides a systematic way to derive explicit residual estimators and estimators based on local problems which are upper and lower bounds of the true error. We show the applications to discretizations of $δd$, curl-curl, grad-div, Hodge Laplacian problems, and linear elasticity with weak symmetry. We also provide a new regular decomposition for singularly perturbed H(d) norms and parameter-independent error estimators. The only ingredients needed are: well-posedness of the problem and the existence of regular decomposition on continuous level.
