A novel spectral method and error analysis for fourth-order equations in a spherical region

Ting Tan, Lan Li and Jing An

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 200, issue C, 148-161

Abstract: We propose a novel spectral-Galerkin approximation of the fourth-order equations in a spherical region. Under spherical coordinate conversion, we reduce the original problem to a set of independent one-dimensional forms by using the orthogonal property of the spherical harmonic functions. The spherical coordinate conversion introduces a singular coefficient, making the theoretical analysis difficult. We present some appropriate weighted Sobolev spaces with the corresponding polar conditions and establish the weak form and its related discrete scheme to overcome these difficulties. Then, we define some new projection operators, prove their approximation properties, and give the approximation results for the numerical solutions. Finally, we present some numerical examples to assess the convergence and spectral accuracy of the proposed algorithm.

Keywords: Fourth-order equation; Polar condition and weighted Sobolev space; Spectral-Galerkin method; Error estimation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:200:y:2022:i:c:p:148-161

DOI: 10.1016/j.matcom.2022.04.017

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