{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T07:55:59Z","timestamp":1653378959969},"reference-count":94,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is still an open problem to prove<jats:italic>a priori<\/jats:italic>error estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domain<jats:italic>\u03a9<\/jats:italic>in \u211d<jats:sup>2<\/jats:sup>and we can prove such kind of an<jats:italic>a priori<\/jats:italic>error estimate. In the part of the estimate, which refers to the discretization of the convective term, we gain<jats:italic>h<\/jats:italic><jats:sup>1\/2<\/jats:sup>. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction\/limiter technique.<\/jats:p>","DOI":"10.1515\/jnma-2016-1056","type":"journal-article","created":{"date-parts":[[2017,2,5]],"date-time":"2017-02-05T10:05:18Z","timestamp":1486289118000},"page":"35-62","source":"Crossref","is-referenced-by-count":1,"title":["Error estimates for higher-order finite volume schemes for convection\u2013diffusion problems"],"prefix":"10.1515","volume":"26","author":[{"given":"Dietmar","family":"Kr\u00f6ner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mirko","family":"Rokyta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"ref541","doi-asserted-by":"crossref","first-page":"4021","DOI":"10.1137\/080720164","article-title":"A new class of high order finite volume methods for second order elliptic equations","volume":"47","year":"2010","journal-title":"SIAM J. 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