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Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations

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Abstract

In this paper, we investigate the application of the fading regularization method with the method of fundamental solutions (MFS) to the ill-posed Cauchy-Stokes problem. For both smooth and piecewise smooth two-dimensional geometries, we present a numerical reconstruction of the missing velocity and normal stress tensor on an inaccessible part of the boundary based on knowledge of over-prescribed noisy data acquired on the remaining accessible boundary part. Three numerical examples demonstrate the proposed numerical algorithm’s accuracy, convergence, stability, and efficiency, as well as its ability to deblur the data.

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Acknowledgements

Hatem Zayeni thanks the Tunisian government for the work-study scholarships in order to carry out part of this research in France at the University of Caen-Normandy.

Funding

Campus France, PHC Utique -CMCU 20G1501- Campus France 44300SD

Author information

Authors and Affiliations

  1. University of Tunis El Manar, National Engineering School of Tunis, LAMSIN 1002, Tunis, Tunisia

    Hatem Zayeni, Amel Ben Abda & Faten Khayat

  2. Normandie Univ, UNICAEN, CNRS, LMNO, 14000, Caen, France

    Franck Delvare

Authors
  1. Hatem Zayeni
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  2. Amel Ben Abda
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  3. Franck Delvare
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  4. Faten Khayat
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Contributions

A.B.A. and F.D. conceived the original idea. H.Z. developed the theoretical formalism, performed the analytic calculations and the numerical simulations. A.B.A, F.D. and F.K. supervised the project. H.Z. wrote the main manuscript text and all authors reviewed the manuscript.

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Correspondence to Franck Delvare.

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Zayeni, H., Abda, A.B., Delvare, F. et al. Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations. Numer Algor 94, 1461–1488 (2023). https://doi.org/10.1007/s11075-023-01543-8

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  • DOI: https://doi.org/10.1007/s11075-023-01543-8

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