Mixed finite elements for the Gross-Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound

被引：0

作者：

Gallistl, Dietmar ^{[1
]}

Hauck, Moritz ^{[2
,3
]}

Liang, Yizhou ^{[4
]}

Peterseim, Daniel ^{[4
,5
]}

机构：

[1] Univ Jena, Inst Math, Ernst Abbe Pl 2, D-07743 Jena, Germany

[2] Univ Gothenburg, Dept Math Sci, S-41296 Gothenburg, Sweden

[3] Chalmers Univ Technol, S-41296 Gothenburg, Sweden

[4] Univ Augsburg, Inst Math, Univ Str 12a, D-86159 Augsburg, Germany

[5] Univ Augsburg, Ctr Adv Analyt & Predict Sci CAAPS, Univ Str 12a, D-86159 Augsburg, Germany

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2025年 / 45卷 / 03期

基金：

欧洲研究理事会;

关键词：

Gross-Pitaevskii eigenvalue problem; mixed finite elements; lower bounds; a priori error analysis; GROUND-STATE SOLUTION; SOBOLEV GRADIENT FLOW; CONVERGENCE; LOCALIZATION; SUPERCONVERGENCE; COMPUTATION;

D O I：

10.1093/imanum/drae048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish an a priori error analysis for the lowest-order Raviart-Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.

引用

页码：1320 / 1346

页数：27

共 47 条

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