Enriched \(P_1\)-conforming methods for elliptic interface problems with implicit jump conditions
type: Item
instance of: scholarly article
title: Enriched \(P_1\)-conforming methods for elliptic interface problems with implicit jump conditions
zbMATH Open document ID: 1440.65213
DOI: 10.1155/2018/9891281
author: Gwanghyun Jo
author: Do Y. Kwak
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We develop a numerical method for elliptic interface problems with implicit jumps. To handle the discontinuity, we enrich usual \(P_1\)-conforming finite element space by adding extra degrees of freedom on one side of the interface. Next, we define a new bilinear form, which incorporates the implicit jump conditions. We show that the bilinear form is coercive and bounded if the penalty term is sufficiently large. We prove the optimal error estimates in both energy-like norm and \(L^2\)-norm. We provide numerical experiments. We observe that our scheme converges with optimal rates, which coincides with our error analysis.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6992050
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9891281
OpenAlex ID: W2802861357
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description: scientific article; zbMATH DE number 6992050