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math.NA2024
On inf-sup stability and optimal convergence of the quasi-reversibility method for unique continuation subject to Poisson's equation
Erik Burman, Mingfei Lu
In this paper, we develop a framework for the discretization of a mixed formulation of quasi-reversibility solutions to ill-posed problems with respect to Poisson's equations. By c…
math.NA2024
Solving the unique continuation problem for Schrödinger equations with low regularity solutions using a stabilized finite element method
Erik Burman, Mingfei Lu, Lauri Oksanen
In this paper, we consider the unique continuation problem for the Schrödinger equations. We prove a Hölder type conditional stability estimate and build up a parameterized stabili…
math.NA2024★ 1 cited
Computational unique continuation with finite dimensional Neumann trace
Erik Burman, Lauri Oksanen, Ziyao Zhao
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 re…