A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability

Carlos Castro; Sorin Micu

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arXiv · 2501.11352

A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability

Carlos Castro·Sorin Micu

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Abstract

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem using a space discretization based on a mixed finite element method is proposed and analyzed. Its stability and convergence relay on a new uniform boundary observability property with respect to the discretization parameter.

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Carlos Castro, Sorin Micu. 2025-01-20. A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability. https://arxiv.org/abs/2501.11352

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