Finite element approximation of spectral problems with Neumann boundary conditions on curved domains

Hernández, Erwin; Rodríguez, Rodolfo

doi:10.1090/S0025-5718-02-01467-9

Finite element approximation of spectral problems with Neumann boundary conditions on curved domains
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by Erwin Hernández and Rodolfo Rodríguez;

Math. Comp. 72 (2003), 1099-1115

DOI: https://doi.org/10.1090/S0025-5718-02-01467-9

Published electronically: December 3, 2002

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Abstract:

This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain $\Omega$. Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain $\Omega _h\not \subset \Omega$ in the framework of the abstract spectral approximation theory.

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