scholarly journals A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method

2021 ◽  
Vol 2 (4) ◽  
pp. 776-792
Author(s):  
Yingxia Xi & Xia Ji
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Operator Function ◽  
Function Approach ◽  
Holomorphic Operator ◽  
Laplace Eigenvalue ◽  
Holomorphic Operator Function

C0IPG for a Fourth Order Eigenvalue Problem

2016 ◽  
Vol 19 (2) ◽  
pp. 393-410 ◽  
Author(s):  
Xia Ji ◽  
Hongrui Geng ◽  
Jiguang Sun ◽  
Liwei Xu
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Method ◽  
Numerical Computation ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Fourth Order ◽  
Well Posedness ◽  
Numerical Examples ◽  
Fourth Order Eigenvalue Problem ◽  
Lagrange Elements

AbstractThis paper concerns numerical computation of a fourth order eigenvalue problem. We first show the well-posedness of the source problem. An interior penalty discontinuous Galerkin method (C0IPG) using Lagrange elements is proposed and its convergence is studied. The method is then used to compute the eigenvalues. We show that the method is spectrally correct and prove the optimal convergence. Numerical examples are presented to validate the theory.

SELECTION OF VISCOUS TERMS APPROXIMATION IN DISCONTINUOUS GALERKIN METHOD

2013 ◽  
Vol 44 (3) ◽  
pp. 327-354
Author(s):  
Aleksey Igorevich Troshin ◽  
Vladimir Viktorovich Vlasenko ◽  
Andrey Viktorovich Wolkov
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
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