Abstract
The boundary value problem of Helmholtz's equation on a n + 1 dimensional thin slab is approximated by appropriate systems of the n-dimensional boundary value problem. The very detailed estimates for modeling error in the H1-norm demonstrate convergence when the thickness of the slab approaches 0 as well as when the size of the systems approaches infinity. Shape functions through the thickness are first selected by finitely many eigenfunctions, and the tail is then selected to consist of polynomials. The presence of two types of functions gives rise to a certain choice in the selection of a particular set of shape functions. Numerical results provide a good illustration of the effect of different choices for specific problems.
| Original language | English |
|---|---|
| Pages (from-to) | 169-190 |
| Number of pages | 22 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1999 Mar |
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All Science Journal Classification (ASJC) codes
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
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Selections of shape functions for dimensional reduction to Helmholtz's equation. / Liu, Kang Man; Babuška, Ivo.
In: Numerical Methods for Partial Differential Equations, Vol. 15, No. 2, 03.1999, p. 169-190.Research output: Contribution to journal › Article
TY - JOUR
T1 - Selections of shape functions for dimensional reduction to Helmholtz's equation
AU - Liu, Kang Man
AU - Babuška, Ivo
PY - 1999/3
Y1 - 1999/3
N2 - The boundary value problem of Helmholtz's equation on a n + 1 dimensional thin slab is approximated by appropriate systems of the n-dimensional boundary value problem. The very detailed estimates for modeling error in the H1-norm demonstrate convergence when the thickness of the slab approaches 0 as well as when the size of the systems approaches infinity. Shape functions through the thickness are first selected by finitely many eigenfunctions, and the tail is then selected to consist of polynomials. The presence of two types of functions gives rise to a certain choice in the selection of a particular set of shape functions. Numerical results provide a good illustration of the effect of different choices for specific problems.
AB - The boundary value problem of Helmholtz's equation on a n + 1 dimensional thin slab is approximated by appropriate systems of the n-dimensional boundary value problem. The very detailed estimates for modeling error in the H1-norm demonstrate convergence when the thickness of the slab approaches 0 as well as when the size of the systems approaches infinity. Shape functions through the thickness are first selected by finitely many eigenfunctions, and the tail is then selected to consist of polynomials. The presence of two types of functions gives rise to a certain choice in the selection of a particular set of shape functions. Numerical results provide a good illustration of the effect of different choices for specific problems.
UR - http://www.scopus.com/inward/record.url?scp=0009726479&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0009726479&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1098-2426(199903)15:2<169::AID-NUM3>3.0.CO;2-X
DO - 10.1002/(SICI)1098-2426(199903)15:2<169::AID-NUM3>3.0.CO;2-X
M3 - Article
AN - SCOPUS:0009726479
VL - 15
SP - 169
EP - 190
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
SN - 0749-159X
IS - 2
ER -