Enriched P1-conforming methods for elliptic interface problems with implicit jump conditionsopen access
- Authors
- Jo, Gwanghyun; Kwak, Do Y.
- Issue Date
- May-2018
- Publisher
- Hindawi Publishing Corporation
- Citation
- Advances in Mathematical Physics, v.2018, pp 1 - 10
- Pages
- 10
- Indexed
- SCIE
SCOPUS
- Journal Title
- Advances in Mathematical Physics
- Volume
- 2018
- Start Page
- 1
- End Page
- 10
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/115202
- DOI
- 10.1155/2018/9891281
- ISSN
- 1687-9120
1687-9139
- Abstract
- We develop a numerical method for elliptic interface problems with implicit jumps. To handle the discontinuity, we enrich usual P1-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 L2-norm. We provide numerical experiments. We observe that our scheme converges with optimal rates, which coincides with our error analysis. © 2018 Gwanghyun Jo and Do Y. Kwak.
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