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The discrete solution is proved to converge in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>L<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>norm to the unique strong solution to the time-discrete Fisher\u2013KPP equation as the mesh size tends to zero. Numerical experiments in one space dimension illustrate the theoretical results.<\/jats:p>","DOI":"10.1007\/s00211-020-01136-w","type":"journal-article","created":{"date-parts":[[2020,7,25]],"date-time":"2020-07-25T14:03:39Z","timestamp":1595685819000},"page":"119-157","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A structure-preserving discontinuous Galerkin scheme for the Fisher\u2013KPP equation"],"prefix":"10.1007","volume":"146","author":[{"given":"Francesca","family":"Bonizzoni","sequence":"first","affiliation":[]},{"given":"Marcel","family":"Braukhoff","sequence":"additional","affiliation":[]},{"given":"Ansgar","family":"J\u00fcngel","sequence":"additional","affiliation":[]},{"given":"Ilaria","family":"Perugia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,25]]},"reference":[{"key":"1136_CR1","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1051\/m2an\/2017012","volume":"52","author":"A Ait Hammou Oulhaj","year":"2018","unstructured":"Ait Hammou Oulhaj, A., Canc\u00e8s, C., Chainais-Hillairet, C.: Numerical analysis of a nonlinearly stable and positive control volume finite element scheme for Richards equation with anisotropy. 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