Computable Error Estimates for Ground State Solution of Bose-Einstein Condensates

TL;DR

This paper introduces a computable error estimate for the ground state solutions of Bose-Einstein condensates using finite element methods, enabling accurate bounds on eigenvalues and energies.

Contribution

It presents a novel computable error estimate for the Gross-Pitaevskii equation applicable to general meshes, with validation through numerical examples.

Findings

Validated the error estimate with numerical experiments

Derived asymptotic lower bounds for eigenvalues and energies

Demonstrated effectiveness on general meshes

Abstract

In this paper, we propose a computable error estimate of the Gross-Pitaevskii equation for ground state solution of Bose-Einstein condensates by general conforming finite element methods on general meshes. Based on the proposed error estimate, asymptotic lower bounds of the smallest eigenvalue and ground state energy can be obtained. Several numerical examples are presented to validate our theoretical results in this paper.