Volume 2, Issue 4
A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method

Yingxia Xi & Xia Ji

CSIAM Trans. Appl. Math., 2 (2021), pp. 776-792.

Published online: 2021-11

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  • Abstract

The paper presents a holomorphic operator function approach for the Laplace eigenvalue problem using the discontinuous Galerkin method. We rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for the discontinuous Galerkin method is proved by using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method to compute the eigenvalues. Extensive numerical examples are presented to validate the theory.

  • AMS Subject Headings

65N25, 65N30, 47B07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-2-776, author = {Yingxia Xi , and Ji , Xia}, title = {A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2021}, volume = {2}, number = {4}, pages = {776--792}, abstract = {

The paper presents a holomorphic operator function approach for the Laplace eigenvalue problem using the discontinuous Galerkin method. We rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for the discontinuous Galerkin method is proved by using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method to compute the eigenvalues. Extensive numerical examples are presented to validate the theory.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2021-0012}, url = {http://global-sci.org/intro/article_detail/csiam-am/19992.html} }
TY - JOUR T1 - A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method AU - Yingxia Xi , AU - Ji , Xia JO - CSIAM Transactions on Applied Mathematics VL - 4 SP - 776 EP - 792 PY - 2021 DA - 2021/11 SN - 2 DO - http://doi.org/10.4208/csiam-am.SO-2021-0012 UR - https://global-sci.org/intro/article_detail/csiam-am/19992.html KW - Discontinuous Galerkin method, eigenvalue problem, Fredholm operator. AB -

The paper presents a holomorphic operator function approach for the Laplace eigenvalue problem using the discontinuous Galerkin method. We rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for the discontinuous Galerkin method is proved by using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method to compute the eigenvalues. Extensive numerical examples are presented to validate the theory.

Yingxia Xi & Xia Ji. (2021). A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method. CSIAM Transactions on Applied Mathematics. 2 (4). 776-792. doi:10.4208/csiam-am.SO-2021-0012
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