Numerische Mathematik

, Volume 139, Issue 1, pp 1–25 | Cite as

Analysis of Lavrentiev-finite element methods for data completion problems

  • F. Ben BelgacemEmail author
  • V. Girault
  • F. Jelassi


The variational finite element solution of Cauchy’s problem, expressed in the Steklov–Poincaré framework and regularized by the Lavrentiev method, has been introduced and computationally assessed in Azaïez et al. (Inverse Probl Sci Eng 18:1063–1086, 2011). The present work concentrates on the numerical analysis of the semi-discrete problem. We perform the mathematical study of the error to rigorously establish the convergence of the global bias-variance error.

Mathematics Subject Classification

65L09 65F22 65L60 


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Authors and Affiliations

  1. 1.UTC, EA 2222, Laboratoire de Mathématiques Appliquées de CompiègneSorbonne UniversitésCompiegneFrance
  2. 2.UPMC, UMR-CNRS 7598, Laboratoire Jacques-Louis LionsSorbonne UniversitésParisFrance

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