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The goal is to prove consistency and convergence of the approximation on unstructured grids. Consequently, we propose a semi-discrete scheme for the heat equation augmented with Dirichlet, Neumann and Robin boundary conditions. By deriving a priori estimates for the numerical solution, we prove that it converges weakly, and subsequently strongly, to a weak solution of the original problem. A numerical simulation demonstrates that the scheme converges with a second-order rate.<\/jats:p>","DOI":"10.1007\/s10915-023-02256-9","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T16:01:47Z","timestamp":1687276907000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence of Chandrashekar\u2019s Second-Derivative Finite-Volume Approximation"],"prefix":"10.1007","volume":"96","author":[{"given":"Anita","family":"Gjesteland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Magnus","family":"Sv\u00e4rd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"2256_CR1","doi-asserted-by":"crossref","unstructured":"Atkinson, K., Han, W.: Theoretical numerical analysis, a functional analaysis framework. 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