{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:41:05Z","timestamp":1760150465297,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T00:00:00Z","timestamp":1701907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Xinjiang University","award":["XJU2022BS029","12001466"],"award-info":[{"award-number":["XJU2022BS029","12001466"]}]},{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"publisher","award":["XJU2022BS029","12001466"],"award-info":[{"award-number":["XJU2022BS029","12001466"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We present a modified characteristic finite element method that exhibits second-order spatial accuracy for solving convection\u2013reaction\u2013diffusion equations on surfaces. The temporal direction adopted the backward-Euler method, while the spatial direction employed the surface finite element method. In contrast to regular domains, it is observed that the point in the characteristic direction traverses the surface only once within a brief time. Thus, good approximation of the solution in the characteristic direction holds significant importance for the numerical scheme. In this regard, Taylor expansion is employed to reconstruct the solution beyond the surface in the characteristic direction. The stability of our scheme is then proved. A comparison is carried out with an existing characteristic finite element method based on face mesh. Numerical examples are provided to validate the effectiveness of our proposed method.<\/jats:p>","DOI":"10.3390\/e25121631","type":"journal-article","created":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T05:57:08Z","timestamp":1701928628000},"page":"1631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modified Characteristic Finite Element Method with Second-Order Spatial Accuracy for Solving Convection-Dominated Problem on Surfaces"],"prefix":"10.3390","volume":"25","author":[{"given":"Longyuan","family":"Wu","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinlong","family":"Feng","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinnian","family":"He","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"},{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114590","DOI":"10.1016\/j.oceaneng.2023.114590","article-title":"Service life of RC seawall under chloride invasion: A theoretical model incorporating convection-diffusion effect","volume":"279","author":"Lai","year":"2023","journal-title":"Ocean. 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