An HDG method for the Steklov eigenvalue problem. (29th April 2021)

• Record Type: Journal Article
• Authors: Monk, Peter; Zhang, Yangwen
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 3(2022)
• Page Start: 1929
• Page End: 1962
• Publication Date: 2021-04-29
• Subjects: hybridizable discontinuous Galerkin HDG method -- Steklev eigenvalue problem; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab017
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: We propose a hybridizable discontinuous Galerkin (HDG) method for approximating the Steklov eigenvalue problem. We prove optimal convergence rates for the eigenvalues and the eigenfunctions, and under some regularity assumptions we obtain a superconvergent rate for the eigenvalues. Moreover, after we eliminate the flux variable and the scalar variable, the reduced eigenvalue problem is linear and our result holds on any sufficiently regular mesh made of general polyhedral elements. Finally, we present numerical experiments to confirm our theoretical results.