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


Authors: Erwin Hernández and Rodolfo Rodríguez
Journal: Math. Comp. 72 (2003), 1099-1115
MSC (2000): Primary 65N25, 65N30; Secondary 70J30
DOI: https://doi.org/10.1090/S0025-5718-02-01467-9
Published electronically: December 3, 2002
MathSciNet review: 1972729
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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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Additional Information

Erwin Hernández
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: erwin@ing-mat.udec.cl

Rodolfo Rodríguez
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: rodolfo@ing-mat.udec.cl

DOI: https://doi.org/10.1090/S0025-5718-02-01467-9
Keywords: Finite element spectral approximation, curved domains
Received by editor(s): February 2, 2001
Received by editor(s) in revised form: September 28, 2001
Published electronically: December 3, 2002
Additional Notes: The first author was supported by FONDECYT 2000114 (Chile). The second author was partially supported by FONDECYT 1990346 and FONDAP in Applied Mathematics (Chile).
Article copyright: © Copyright 2002 American Mathematical Society

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