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This is a Quantitative Study study.

September 17, 2025Open Access

Computational Unique Continuation with Finite Dimensional Neumann Trace

Puntos clave

Lipschitz stability is established for unique continuation problems based on known normal derivatives.
Error estimates are derived for finite element methods, ensuring reliability in calculations while addressing elliptic equations.
The study focuses on finite dimensional spaces, enhancing the applicability of the primal-dual stabilized method.
This work emphasizes the connection between stability and error estimates, possibly leading to better computational methods.

Resumen

. We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative error estimates we prove Lipschitz stability of the unique continuation problem in the global \ (H¹\) -norm. This stability is then leveraged to derive optimal a posteriori and a priori error estimates for a primal-dual stabilized finite element method. Keywordsunique continuationconditional stabilityfinite dimensionNeumann boundaryfinite element methodsstabilized methodserror estimatesMSC codes65N20

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Cite This Study

Burman et al. (Tue,) studied this question.

synapsesocial.com/papers/68d45e4e31b076d99fa5e540 https://doi.org/https://doi.org/10.1137/24m164080x

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