Work

Solving the unique continuation problem for Schrödinger equations with low regularity solutions using a stabilized finite element method

Year: 2025

Type: article

Abstract: 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 stabilized finite element scheme adaptive to the a priori knowledge of the solution, achieving error estimates in interior domains with convergence up to continuous stability. The approximability of the scheme to solutions with regularity of as low as H1 is studied and the convergence rates for discrete solutions under L2 and H1 norms are shown. Comparisons in terms of different parameterization for different regularities will be illustrated with respect to the convergence and condition numbers of the linear systems. Finally, numerical experiments will be given to illustrate the theory.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025060

Authors: Erik Burman, Mingfei Lu, Lauri Oksanen

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funders: Engineering and Physical Sciences Research Council, H2020 European Research Council

Awards: Quantitative estimates of discretisation and modelling errors in variational data assimilation for incompressible flows, G4277896979, Computational methods for inverse problems subject to wave equations in heterogeneous media