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Enriched -Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions

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  • Gwanghyun Jo
  • Do Y. Kwak

Abstract

We develop a numerical method for elliptic interface problems with implicit jumps. To handle the discontinuity, we enrich usual -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 -norm. We provide numerical experiments. We observe that our scheme converges with optimal rates, which coincides with our error analysis.

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  • Gwanghyun Jo & Do Y. Kwak, 2018. "Enriched -Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-9, May.
    • Handle: RePEc:hin:jnlamp:9891281
    DOI: 10.1155/2018/9891281
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