TY - JOUR
T1 - Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation
AU - Mizuguchi, Makoto
AU - Nakao, Mitsuhiro T.
AU - Sekine, Kouta
AU - Oishi, Shin’ichi
N1 - Funding Information:
This work was supported by CREST, JST Grant No. JPMJCR14D4, JSPS KAKENHI No.18K13462, and JSPS KAKENHI No.18K03434.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/11
Y1 - 2021/11
N2 - In this paper, we propose L2(J;H01(Ω)) and L2(J; L2(Ω ) ) norm error estimates that provide the explicit values of the error constants for the semi-discrete Galerkin approximation of the linear heat equation. The derivation of these error estimates shows the convergence of the approximation to the weak solution of the linear heat equation. Furthermore, explicit values of the error constants for these estimates play an important role in the computer-assisted existential proofs of solutions to semi-linear parabolic partial differential equations. In particular, the constants provided in this paper are better than the existing constants and, in a sense, the best possible.
AB - In this paper, we propose L2(J;H01(Ω)) and L2(J; L2(Ω ) ) norm error estimates that provide the explicit values of the error constants for the semi-discrete Galerkin approximation of the linear heat equation. The derivation of these error estimates shows the convergence of the approximation to the weak solution of the linear heat equation. Furthermore, explicit values of the error constants for these estimates play an important role in the computer-assisted existential proofs of solutions to semi-linear parabolic partial differential equations. In particular, the constants provided in this paper are better than the existing constants and, in a sense, the best possible.
KW - A priori error estimate
KW - Best possible
KW - Error constant
KW - semi-discrete Galerkin approximation
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U2 - 10.1007/s10915-021-01636-3
DO - 10.1007/s10915-021-01636-3
M3 - Article
AN - SCOPUS:85115992273
SN - 0885-7474
VL - 89
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
M1 - 34
ER -