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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.\n<\/jats:p>","DOI":"10.1007\/s10915-021-01636-3","type":"journal-article","created":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T04:12:33Z","timestamp":1632888753000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation"],"prefix":"10.1007","volume":"89","author":[{"given":"Makoto","family":"Mizuguchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitsuhiro T.","family":"Nakao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kouta","family":"Sekine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin\u2019ichi","family":"Oishi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,29]]},"reference":[{"key":"1636_CR1","volume-title":"The Mathematical Theory of Finite Element Methods","author":"S Brenner","year":"2007","unstructured":"Brenner, S., Scott, R.: The Mathematical Theory of Finite Element Methods, 2nd edn. 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