{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T08:40:14Z","timestamp":1718613614223},"reference-count":26,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T00:00:00Z","timestamp":1692144000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,25]]},"abstract":"Abstract<\/jats:title>\n We propose high order conforming and nonconforming immersed hybridized difference (IHD) methods in two and three dimensions for elliptic interface problems. Introducing the virtual to real transformation (VRT), we could obtain a systematic and unique way of deriving arbitrary high order methods in principle. The optimal number of collocating points for imposing interface conditions is proved, and a unique way of constructing the VRT is suggested. Numerical experiments are performed in two and three dimensions. Numerical results achieving up to the 6th order convergence in the L<\/jats:italic>\n 2<\/jats:sub>-norm are presented for the two dimensional case, and a three dimensional example with a 4th order convergence is presented.<\/jats:p>","DOI":"10.1515\/jnma-2023-0011","type":"journal-article","created":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T22:00:49Z","timestamp":1692223249000},"page":"139-156","source":"Crossref","is-referenced-by-count":0,"title":["High order immersed hybridized difference methods for elliptic interface problems"],"prefix":"10.1515","volume":"32","author":[{"given":"Youngmok","family":"Jeon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ajou University , Suwon , Korea"}]}],"member":"374","published-online":{"date-parts":[[2023,8,16]]},"reference":[{"key":"2024061708160708024_j_jnma-2023-0011_ref_001","doi-asserted-by":"crossref","unstructured":"S. Adjerid, I. Babu\u0161ka, R. Guo, and T. 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