C0IPG for a Fourth Order Eigenvalue Problem. (1st February 2016)

• Record Type: Journal Article
• Authors: Ji, Xia; Geng, Hongrui; Sun, Jiguang; Xu, Liwei
• Is Part Of: Communications in computational physics. Volume 19:Number 2(2016:Feb.)
• Page Start: 393
• Page End: 410
• Publication Date: 2016-02-01
• Subjects: 65N25, -- 65N30, -- 65N22; Fourth order eigenvalue problem, -- discontinuous Galerkin method, -- spectrum approximation; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.131014.140715a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: This 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 (C 0 IPG) 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.