The weak Galerkin method for a class of Gross-Pitaevskii type eigenvalue problems

Abstract

This paper aims to employ the weak Galerkin method to solve a class of nonlinear eigenvalue problems. We proved the weak Galerkin scheme produces lower bound for the energy. Moreover, by the post-processing technique, we obtain lower bound for the ground state eigenvalue. Finally, numerical experiments are provided to validate the theoretical analysis.