Finite element method for an eigenvalue optimization problem of the Schrödinger operator

• Published in: AIMS mathematics Vol. 7; no. 4; pp. 5049 - 5071
• Main Authors: Guo, Shuangbing, Lu, Xiliang, Zhang, Zhiyue
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2022
• Subjects: eigenvalue optimization; error estimate; finite element method; schrödinger operator; shape optimization
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022281

In this paper, we study the optimization algorithm to compute the smallest eigenvalue of the Schrödinger operator with volume constraint. A finite element discretization of this problem is established. We provide the error estimate for the numerical solution. The optimal solution can be approximated...