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PreprintCC BY 4.0arXiv

Beyond the analytic solution manufacturing for anisotropic elliptic equations

  • Fabrice Deluzet
  • Valdimir Latocha
  • Frédéric Robert
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{deluzet2026beyond,
  title = {{Beyond the analytic solution manufacturing for anisotropic elliptic equations}},
  author = {Fabrice Deluzet and Valdimir Latocha and Frédéric Robert},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36309},
  eprint = {2609.36309},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36309},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Beyond the analytic solution manufacturing for anisotropic elliptic equations
AU  - Fabrice Deluzet
AU  - Valdimir Latocha
AU  - Frédéric Robert
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36309
UR  - https://arxiv.org/abs/2609.36309
AB  - 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.
ER  -