3 papers
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.NA2025
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 stabi…
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…