论文标题
改进的椭圆多尺度问题的高阶方法
An improved high-order method for elliptic multiscale problems
论文作者
论文摘要
在这项工作中，我们提出了一种用于具有粗糙且可能高度振荡系数的椭圆模型问题的高级多尺寸方法。高阶的收敛速率仅使用右侧的规律性获得。因此，需要对系数，域或确切解决方案的限制性假设。本着局部正交分解的精神，该方法通过解决局部子域的辅助问题来构建粗糙的问题适应ANSATZ的空间。更确切地说，我们的方法基于Maier提出的策略[Siam J. Numer。肛门。 59（2），2021]。提出的方法的独特销售点是一种改进的定位策略，可治疗当地子域不够大时，相对于网格大小的误差的影响。我们提出了严格的先验误差分析，并在一系列数值实验中证明了该方法的性能。
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only. Hence, no restrictive assumptions on the coefficient, the domain, or the exact solution are required. In the spirit of the Localized Orthogonal Decomposition, the method constructs coarse problem-adapted ansatz spaces by solving auxiliary problems on local subdomains. More precisely, our approach is based on the strategy presented by Maier [SIAM J. Numer. Anal. 59(2), 2021]. The unique selling point of the proposed method is an improved localization strategy curing the effect of deteriorating errors with respect to the mesh size when the local subdomains are not large enough. We present a rigorous a priori error analysis and demonstrate the performance of the method in a series of numerical experiments.
