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PreprintCC BY-NC-SA 4.0HAL

Study of the finite element discretization of the iterated quasi-reversibility method The Laplacian data assimilation case

  • Jérémi Dardé
  • Jérémy Heleine
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Abstract

We investigate the finite element discretization of the iterated quasi-reversibility method, in the context of the data assimilation problem for the Laplacian. We provide error estimates explicit in all the parameters appearing in the model and the method (i.e. the amplitude of noise, the size mesh, the regularization parameter and the number of iterations of the method). This allows to devise strategies to choose the aforementioned parameters, for example to guarantee convergence of the method when the level of noise goes to zero. Numerical experiments on a two-dimensional problem are provided, illustrating the relevance of the obtained estimates.

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Cite

BibTeXRIS
BibTeX
@misc{darde2026study,
  title = {{Study of the finite element discretization of the iterated quasi-reversibility method The Laplacian data assimilation case}},
  author = {Jérémi Dardé and Jérémy Heleine},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26117},
  eprint = {2610.26117},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05803347v1},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Study of the finite element discretization of the iterated quasi-reversibility method The Laplacian data assimilation case
AU  - Jérémi Dardé
AU  - Jérémy Heleine
PY  - 2026
DA  - 2026/10/16
PB  - HAL
DO  - 10.48550/arxiv.2610.26117
UR  - https://hal.science/hal-05803347v1
AB  - We investigate the finite element discretization of the iterated quasi-reversibility method, in the context of the data assimilation problem for the Laplacian. We provide error estimates explicit in all the parameters appearing in the model and the method (i.e. the amplitude of noise, the size mesh, the regularization parameter and the number of iterations of the method). This allows to devise strategies to choose the aforementioned parameters, for example to guarantee convergence of the method when the level of noise goes to zero. Numerical experiments on a two-dimensional problem are provided, illustrating the relevance of the obtained estimates.
ER  -