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math.NA2025
Alleviating missing boundary conditions in elliptic partial differential equations using interior point measurements
Andrea Bonito, Alan Demlow, Joshua M. Siktar
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measuremen…
math.NA2024
-convergence of an Enhanced Finite Element Method for Manià's and Foss's Problems Exhibiting the Lavrentiev Gap Phenomenon
Xiaobing Feng, Joshua M. Siktar
It is well-known that numerically approximating calculus of variations problems possessing a Lavrentiev Gap Phenomenon (LGP) is challenging, and the standard numerical methodologie…