TY - JOUR
T1 - Some improvements of invertibility verifications for second-order linear elliptic operators
AU - Watanabe, Yoshitaka
AU - Kinoshita, Takehiko
AU - Nakao, Mitsuhiro T.
N1 - Funding Information:
The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15K05012, 15H03637) and Japan Science and Technology Agency, CREST (No. JPMJCR14D4). The computation was mainly carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University, Japan.
Funding Information:
The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15K05012 , 15H03637 ) and Japan Science and Technology Agency , CREST (No. JPMJCR14D4 ). The computation was mainly carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University, Japan.
Publisher Copyright:
© 2020 IMACS
PY - 2020/8
Y1 - 2020/8
N2 - This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L2-norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported.
AB - This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L2-norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported.
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U2 - 10.1016/j.apnum.2020.03.016
DO - 10.1016/j.apnum.2020.03.016
M3 - Article
AN - SCOPUS:85082122571
SN - 0168-9274
VL - 154
SP - 36
EP - 46
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -