Numerical analysis of linear finite element methods for the Gross--Pitaevskii eigenvalue problem

arXiv:2610.41715v1 Announce Type: new Abstract: In this paper, we analyze the standard and the mass-lumped linear finite element methods for the Gross--Pitaevskii eigenvalue problem. For the standard method, we give a new proof of the uniqueness of the discrete ground state up to sign for sufficiently small mesh sizes, which only requires the $H^1$-convergence of the discrete ground states. For both methods, we establish optimal convergence rates in the $L^p$- and $W^{1,p}$-norms for $1 \le p