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Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.\n<\/jats:p>","DOI":"10.1007\/s00211-021-01240-5","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T18:02:50Z","timestamp":1637604170000},"page":"79-103","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations"],"prefix":"10.1007","volume":"150","author":[{"given":"V\u00e1clav","family":"Ku\u010dera","sequence":"first","affiliation":[]},{"given":"M\u00e1ria","family":"Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1","sequence":"additional","affiliation":[]},{"given":"Sebastian","family":"Noelle","sequence":"additional","affiliation":[]},{"given":"Jochen","family":"Sch\u00fctz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"key":"1240_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-020-01138-8","volume":"82","author":"KR Arun","year":"2020","unstructured":"Arun, K.R., Samantaray, S.: Asymptotic preserving low Mach number accurate IMEX finite volume schemes for the isentropic Euler equations. 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