Solving the unique continuation problem for Schrödinger equations with low regularity solutions using a stabilized finite element method
CoRR(2024)
摘要
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 only H^1-regularity is
studied and the convergence rate for solutions with regularity higher than
H^1 is also 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.
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