论文标题
通用非结构化系数的椭圆多尺度问题的高级方法
A high-order approach to elliptic multiscale problems with general unstructured coefficients
论文作者
论文摘要
我们为具有一般非结构化扩散系数的椭圆形多尺度设置提出了一种多尺度方法，该设置能够相对于网格参数和多项式程度实现高阶收敛速率。该方法允许合适的定位，并且不依赖于域，扩散系数或精确（弱）解决方案的其他规则性假设，这是高阶方法通常所需的。严格的先验误差估计是相对于所涉及的离散参数的，这些参数以及该方法的性能之间的相互作用进行了数值研究。
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.
