Abstract
In this paper, we show some constructive a priori error estimates for H0 2-projection into a space of polynomials on a one dimensional interval. Here, 'constructive' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H0 2- projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.
| Original language | English |
|---|---|
| Title of host publication | Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 |
| Pages | 926-929 |
| Number of pages | 4 |
| Volume | 1168 |
| DOIs | |
| Publication status | Published - 2009 |
| Externally published | Yes |
| Event | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece Duration: 2009 Sep 18 → 2009 Sep 22 |
Other
| Other | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 |
|---|---|
| Country | Greece |
| City | Rethymno, Crete |
| Period | 09/9/18 → 09/9/22 |
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Keywords
- Constructive a priori error estimates
- Fourth order elliptic problem
- Legendre polynomials
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
On verified computations of the optimal constant in the a priori error estimates for h0 2-projection. / Nakao, Mitsuhiro T.; Kinoshita, Takehiko.
Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. Vol. 1168 2009. p. 926-929.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - On verified computations of the optimal constant in the a priori error estimates for h0 2-projection
AU - Nakao, Mitsuhiro T.
AU - Kinoshita, Takehiko
PY - 2009
Y1 - 2009
N2 - In this paper, we show some constructive a priori error estimates for H0 2-projection into a space of polynomials on a one dimensional interval. Here, 'constructive' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H0 2- projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.
AB - In this paper, we show some constructive a priori error estimates for H0 2-projection into a space of polynomials on a one dimensional interval. Here, 'constructive' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H0 2- projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.
KW - Constructive a priori error estimates
KW - Fourth order elliptic problem
KW - Legendre polynomials
UR - http://www.scopus.com/inward/record.url?scp=70450175229&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70450175229&partnerID=8YFLogxK
U2 - 10.1063/1.3241634
DO - 10.1063/1.3241634
M3 - Conference contribution
AN - SCOPUS:70450175229
SN - 9780735407091
VL - 1168
SP - 926
EP - 929
BT - Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
ER -