发表机构
Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, CNRS; Université de Lorraine, CNRS, IECL（图卢兹大学；数学研究所; 洛林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于黎曼度量和边界值传播的新方法，用于构造各向异性椭圆方程的参考解，突破了传统解析解构造的限制，扩展了适用范围。
AI 中文摘要
本文旨在引入一种新程序来定义参考解，等离子体物理中出现的各向异性问题的数值近似可与之比较。在此背景下，主要问题与构造沿定义各向异性方向的向量场无梯度的函数相关。迄今为止文献中实施的所谓解构造方法仅适用于所有计算均可解析进行的框架。在本文中，我们提出一种新方法，其中该要求并非强制。实际上，通过黎曼度量，我们利用与定义各向异性方向的向量场相关的流来传播边界值。这使得解构造方法能够应用于更广泛的背景。
英文摘要
This article is aimed at introducing a new procedure to define reference solutions to which the numerical approximations of anisotropic problems arising in plasma physics may be compared. In this context, the main issue is related to the construction of functions with no gradients along the vector field defining the anisotropy direction. The so-called solution manufacturing, implemented so far in the literature, only applies to frame- work where all the computations can be carried out analytically. In the present paper, we propose a new method in which this requirement is not mandatory. Indeed, via a Riemannian metric, we use a propagation of the boundary value by the flows related to the vector field defining the anisotropy direction. This permits to extend the application of the solution manufacturing to a broader range of contexts.
