标题： 保持离散各向异性椭圆问题数值方法的精度 显示英文标题

标题： Preserving the accuracy of numerical methods discretizing anisotropic elliptic problems

摘要： 在本文中，我们研究了离散各向异性问题的数值方法的精度损失，并提出了避免这一缺点的替代方法。 当坐标和网格与各向异性方向无关时，会观察到精度的下降。 虽然通常通过增加格式的近似阶数来解决此问题，但我们证明，尽管收益明显，这些数值方法的精度仍远非最优，并且仅限于中等各向异性强度。 这是通过与各向异性强度相关的近似误差放大来分析和解释的。 我们提出了一种方法，即引入一个辅助变量，旨在消除离散误差的放大。 通过这种方法，数值近似的精度被证明与各向异性强度无关。 显示英文摘要

摘要： In this paper we study the loss of precision of numerical methods discretizing anisotropic problems and propose alternative approaches free from this drawback. The deterioration of the accuracy is observed when the coordinates and the mesh are unrelated to the anisotropy direction. While this issue is commonly addressed by increasing the scheme approximation order, we demonstrate that, though the gains are evident, the precision of these numerical methods remain far from optimal and limited to moderate anisotropy strengths. This is analysed and explained by an amplification of the approximation error related to the anisotropy strength. We propose an approach consisting in the introduction of an auxiliary variable aimed at removing the amplification of the discretization error. By this means the precision of the numerical approximation is demonstrated to be independent of the anisotropy strength.