Abstract
In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.
| Original language | English |
|---|---|
| Pages (from-to) | 1-14 |
| Number of pages | 14 |
| Journal | Computing (Vienna/New York) |
| Volume | 75 |
| Issue number | 1 SPEC. ISS. |
| DOIs | |
| Publication status | Published - 2005 Jul |
| Externally published | Yes |
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Keywords
- Finite element method
- Numerical verification
- Unique solvability of linear elliptic problem
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Theory and Mathematics
Cite this
A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. / Nakao, M. T.; Hashimoto, K.; Watanabe, Y.
In: Computing (Vienna/New York), Vol. 75, No. 1 SPEC. ISS., 07.2005, p. 1-14.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
AU - Nakao, M. T.
AU - Hashimoto, K.
AU - Watanabe, Y.
PY - 2005/7
Y1 - 2005/7
N2 - In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.
AB - In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.
KW - Finite element method
KW - Numerical verification
KW - Unique solvability of linear elliptic problem
UR - http://www.scopus.com/inward/record.url?scp=23744514537&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=23744514537&partnerID=8YFLogxK
U2 - 10.1007/s00607-004-0111-1
DO - 10.1007/s00607-004-0111-1
M3 - Article
AN - SCOPUS:23744514537
VL - 75
SP - 1
EP - 14
JO - Computing
JF - Computing
SN - 0010-485X
IS - 1 SPEC. ISS.
ER -