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math.NA2025
Posterior contraction rates of computational methods for Bayesian data assimilation
Erik Burman, Mingfei Lu
In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth…
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…