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

Authors:
Erwin Hernández;Rodolfo Rodríguez
Affiliations:
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile;Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Venue:
Mathematics of Computation
Year:
2003

Citing 7
Cited 2

Finite element solution of nonlinear elliptic problems

Numerische Mathematik
Optimal finite-element interpolation on curved domains

SIAM Journal on Numerical Analysis
A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries

Mathematics of Computation
Error estimate in an isoparametric finite element eigenvalue problem

Mathematics of Computation
External finite-element approximations of eigenfunctions in the case of multiple eigenvalues

ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
The combined effect of numerical integration and approximation of the boundary in the finite element method for eigenvalue problems

Numerische Mathematik
On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form

Mathematics of Computation

Finite element approximation of the elasticity spectral problem on curved domains

Journal of Computational and Applied Mathematics
Convergence analysis for eigenvalue approximations on triangular finite element meshes

NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications

Quantified Score

Hi-index	0.00

Visualization

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 Ω. Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain Ωh ⊄ Ω in tile framework of the abstract spectral approximation theory.