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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |