TY - JOUR
T1 - Inclusion method of optimal constant with quadratic convergence for H01-projection error estimates and its applications
AU - Kinoshita, Takehiko
AU - Watanabe, Yoshitaka
AU - Yamamoto, Nobito
AU - Nakao, Mitsuhiro T.
N1 - Funding Information:
The authors heartily thank the 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. 15H03637 , 16H03950 , 18K03410 , 18K03434 , 21H01000 , 21K03348 , 21K03373 , 21K03378 ) 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 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. 15H03637, 16H03950, 18K03410, 18K03434, 21H01000, 21K03348, 21K03373, 21K03378) 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:
© 2022 The Author(s)
PY - 2023/1/1
Y1 - 2023/1/1
N2 - We present an interval inclusion method for optimal constants of second-order error estimates of H01-projections to finite-degree polynomial spaces. These constants can be applied to error estimates of the Lagrange-type finite element method. Moreover, the proposed a priori error estimates are applicable to residual iteration techniques for the verification of solutions to nonlinear elliptic equations. Some numerical examples by the finite element method will be shown for comparison with other approaches, which confirm us the actual usefulness of the results in this paper for the numerical verification method for PDEs.
AB - We present an interval inclusion method for optimal constants of second-order error estimates of H01-projections to finite-degree polynomial spaces. These constants can be applied to error estimates of the Lagrange-type finite element method. Moreover, the proposed a priori error estimates are applicable to residual iteration techniques for the verification of solutions to nonlinear elliptic equations. Some numerical examples by the finite element method will be shown for comparison with other approaches, which confirm us the actual usefulness of the results in this paper for the numerical verification method for PDEs.
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U2 - 10.1016/j.cam.2022.114521
DO - 10.1016/j.cam.2022.114521
M3 - Article
AN - SCOPUS:85135374226
SN - 0377-0427
VL - 417
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 114521
ER -