Rate of convergence estimates for second order elliptic eigenvalue problems on polygonal domains using spectral element methods

Lokendra K. Balyana,1, Subir Singh Lambab

a,bDepartment of Mathematics, IIIT-DM Jabalpur, India
1Corresponding author: E-mail: lokendra.balyan@gmail.com

Abstract: In this paper, we present rate of convergence estimates for eigenvalues and eigenvectors of elliptic differential operators on non-smooth domains using non-conforming spectral element methods. We define a class of compact operators on Banach space which is used to obtain the results. If coefficients of the differential operator are sufficiently smooth and the boundaries of the polygonal domain are piecewise analytic then exponential convergence to approximate solution is obtained.

Keywords: Rate of convergence; eigenvalues and eigenvectors; non-smooth domains; singularities; $h$-$p$ spectral element method.

MSC: 35Jxx; 35Pxx

 

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