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A numerical approach for investigating multiple eigenpairs of a quasilinear elliptic system

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Abstract

The aim of this study is to provide a rigorous description of a numerical approach based on the local min-orthogonal method for finding multiple eigenpairs of a quasilinear elliptic system. By a Rayleigh quotient formulation, the eigenvalue problem is transformed into a constrained variational problem. In this constrained problem setup, we define a novel local L-\(\perp \) selection mapping on a product space of two Banach spaces in order to develop a local characterization of the eigenfunctions. Based on this local characterization, we present a numerical algorithm for computing multiple eigenpairs of the quasilinear elliptic system. For practical implementation of the proposed algorithm, we discretized the eigenvalue problem using the finite element method. Then, a global sequence convergence result of the algorithm is established for the discretized problem. Finally, the algorithm and its associated theory are demonstrated by numerical experiments.

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Acknowledgements

The author would like to acknowledge Dr. Sudhakar Chaudhary for several helpful discussions and suggestions. The author would also like to thank the anonymous reviewers for many helpful suggestions and comments.

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  1. Suchismita Patra

    Present address: Department of Mathematics, School of Advanced Sciences & Languages, VIT Bhopal University, Ashta, Bhopal, Madhya Pradesh, India

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  1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

    Suchismita Patra

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Patra, S. A numerical approach for investigating multiple eigenpairs of a quasilinear elliptic system. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01822-y

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