Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions
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 jum...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/9891281 |
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| _version_ | 1832566490624163840 |
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| author | Gwanghyun Jo Do Y. Kwak |
| author_facet | Gwanghyun Jo Do Y. Kwak |
| author_sort | Gwanghyun Jo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8d325d850dd845fa88275e7db51cd171 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8d325d850dd845fa88275e7db51cd1712025-02-03T01:04:02ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/98912819891281Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump ConditionsGwanghyun Jo0Do Y. Kwak1Department of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of KoreaDepartment of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of KoreaWe 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.http://dx.doi.org/10.1155/2018/9891281 |
| spellingShingle | Gwanghyun Jo Do Y. Kwak Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions Advances in Mathematical Physics |
| title | Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions |
| title_full | Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions |
| title_fullStr | Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions |
| title_full_unstemmed | Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions |
| title_short | Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions |
| title_sort | enriched p1 conforming methods for elliptic interface problems with implicit jump conditions |
| url | http://dx.doi.org/10.1155/2018/9891281 |
| work_keys_str_mv | AT gwanghyunjo enrichedp1conformingmethodsforellipticinterfaceproblemswithimplicitjumpconditions AT doykwak enrichedp1conformingmethodsforellipticinterfaceproblemswithimplicitjumpconditions |