SIAM Journal on Numerical Analysis, Volume 59, Issue 2, Page 1067-1089, January 2021.
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The method allows for suitable localization and does not rely on additional regularity assumptions on the domain, the diffusion coefficient, or the exact (weak) solution as typically required for high-order approaches. Rigorous a priori error estimates are presented with respect to the involved discretization parameters, and the interplay between these parameters as well as the performance of the method are studied numerically.

中文翻译：

---

具有一般非结构系数的椭圆多尺度问题的高阶方法

SIAM数值分析杂志，第59卷，第2期，第1067-1089页，2021年1月。
我们提出了一种椭圆形多尺度设置的多尺度方法，该方法具有一般的非结构化扩散系数，能够实现相对于网格的高阶收敛速率参数和多项式次数。该方法允许适当的定位，并且不依赖于域，扩散系数或高阶方法通常所需的精确（弱）解的其他正则性假设。针对所涉及的离散化参数，给出了严格的先验误差估计，并对这些参数之间的相互作用以及该方法的性能进行了数值研究。