SOLVING PDES WITH INCOMPLETE INFORMATION - Université de Paris - Faculté des Sciences Access content directly
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Peter Binev
  • Function : Author
Andrea Bonito
  • Function : Author
Albert Cohen
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  • PersonId : 1124843
Wolfgang Dahmen
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Ronald Devore
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Guergana Petrova
  • Function : Author


We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when the boundary data is unknown and instead one observes finitely many linear measurements of the solution. We view this setting as an optimal recovery problem and develop theory and numerical algorithms for its solution. The main vehicle employed is the derivation and approximation of the Riesz representers of these functionals with respect to relevant Hilbert spaces of harmonic functions.
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hal-04031972 , version 1 (16-03-2023)


  • HAL Id : hal-04031972 , version 1


Peter Binev, Andrea Bonito, Albert Cohen, Wolfgang Dahmen, Ronald Devore, et al.. SOLVING PDES WITH INCOMPLETE INFORMATION. 2023. ⟨hal-04031972⟩
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