Abstract
In this work, we consider the behaviour of the residual error using a smooth finite element solution for elliptic problems on nonconvex and nonsmooth domains. It is proved that, against expectations, the residual error is unbounded and actually diverges to infinity as the mesh size goes to zero. A numerical example which illustrates this phenomenon will be presented for the Poisson equation on an L-shaped domain using a C1 Hermite element, and similar results will be shown for a C0 element with a posteriori smoothing.
| Original language | English |
|---|---|
| Pages (from-to) | 1310-1314 |
| Number of pages | 5 |
| Journal | Applied Mathematics Letters |
| Volume | 21 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2008 Dec |
| Externally published | Yes |
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Keywords
- Nonsmooth domain
- Poisson equation
- Residual error
ASJC Scopus subject areas
- Applied Mathematics
Cite this
Some remarks on the behaviour of the finite element solution in nonsmooth domains. / Nakao, Mitsuhiro T.; Kinoshita, Takehiko.
In: Applied Mathematics Letters, Vol. 21, No. 12, 12.2008, p. 1310-1314.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Some remarks on the behaviour of the finite element solution in nonsmooth domains
AU - Nakao, Mitsuhiro T.
AU - Kinoshita, Takehiko
PY - 2008/12
Y1 - 2008/12
N2 - In this work, we consider the behaviour of the residual error using a smooth finite element solution for elliptic problems on nonconvex and nonsmooth domains. It is proved that, against expectations, the residual error is unbounded and actually diverges to infinity as the mesh size goes to zero. A numerical example which illustrates this phenomenon will be presented for the Poisson equation on an L-shaped domain using a C1 Hermite element, and similar results will be shown for a C0 element with a posteriori smoothing.
AB - In this work, we consider the behaviour of the residual error using a smooth finite element solution for elliptic problems on nonconvex and nonsmooth domains. It is proved that, against expectations, the residual error is unbounded and actually diverges to infinity as the mesh size goes to zero. A numerical example which illustrates this phenomenon will be presented for the Poisson equation on an L-shaped domain using a C1 Hermite element, and similar results will be shown for a C0 element with a posteriori smoothing.
KW - Nonsmooth domain
KW - Poisson equation
KW - Residual error
UR - http://www.scopus.com/inward/record.url?scp=53049085391&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=53049085391&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2007.11.005
DO - 10.1016/j.aml.2007.11.005
M3 - Article
AN - SCOPUS:53049085391
VL - 21
SP - 1310
EP - 1314
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
SN - 0893-9659
IS - 12
ER -