๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition

โœ Scribed by Daisuke Koyama

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
795 KB
Volume
232
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

โœฆ Synopsis

A priori error estimates in the H 1 -and L 2 -norms are established for the finite element method applied to the exterior Helmholtz problem, with modified Dirichlet-to-Neumann (MDtN) boundary condition. The error estimates include the effect of truncation of the MDtN boundary condition as well as that of discretization of the finite element method. The error estimate in the L 2 -norm is sharper than that obtained by the author [D. Koyama, Error estimates of the DtN finite element method for the exterior Helmholtz problem, J. Comput. Appl. Math. 200 (1) (2007) 21-31] for the truncated DtN boundary condition.

๐Ÿ“œ SIMILAR VOLUMES

THE THREE-DIMENSIONAL DtN FINITE ELEMENT
THE THREE-DIMENSIONAL DtN FINITE ELEMENT METHOD FOR RADIATION PROBLEMS OF THE HELMHOLTZ EQUATION
โœ D. Giljohann; M. Bittner ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 254 KB

A finite element method is presented for solving three-dimensional radiation problems in time-harmonic acoustics. This is done by introducing a so-called ''Dirichlet-to-Neumann'' boundary condition on the outer boundary of the domain discretized with finite elements. This DtN boundary condition is a

Nonlinear artificial boundary conditions
Nonlinear artificial boundary conditions with pointwise error estimates for the exterior three dimensional Navierโ€“Stokes problem
โœ Sergej A. Nazarov; Maria Specoviusโ€“Neugebauer ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 282 KB

## Abstract On a threeโ€“dimensional exterior domain ฮฉ we consider the Dirichlet problem for the stationary Navierโ€“Stokes system. We construct an approximation problem on the domain ฮฉ~__R__~, which is the intersection of ฮฉ with a sufficiently large ball, while we create nonlinear, but local artificia

Global pointwise error estimates for uni
Global pointwise error estimates for uniformly convergent finite element methods for the elliptic boundary layer problem
โœ J. Li ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 416 KB

This paper continues our discussion for the anisotropic model problem-(e o--~x-{-o--~ ) + a(z, y)u = f(x, y) in [1]. There we constructed a bilinear finite element method on a Shishkin type mesh. The method was shown to be convergent, independent of the small parameter e, in the order of N -2 In 2