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 - <p style="text-align: justify;">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.</p>