The weak Galerkin method for a class of Gross-Pitaevskii type eigenvalue problems
arXiv:2605.2926488.3h-index: 15
AI Analysis
Provides a theoretical guarantee for lower bounds in eigenvalue computations, relevant for numerical analysts working on nonlinear eigenvalue problems.
The authors apply the weak Galerkin method to nonlinear eigenvalue problems, proving it yields lower bounds for energy and ground state eigenvalues, with numerical validation.
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.