Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions

Youngmok Jeon; Dongwook Shin; Youngmok Jeon; Dongwook Shin

doi:10.3934/era.2021043

Electronic Research Archive

2021, Volume 29, Issue 5: 3361-3382. doi: 10.3934/era.2021043

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Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions

Youngmok Jeon ^{1
,
,},
Dongwook Shin ^{2
,}

1.
Department of Mathematics, Ajou University, Suwon 16499, Korea
2.
Department of Mathematics, Myongji University, Yongin 17058, Korea

Received: 01 September 2020 Revised: 01 April 2021 Published: 24 June 2021
Primary: 65L12, 65N06, 65N50

We propose an immersed hybrid difference method for elliptic boundary value problems by artificial interface conditions. The artificial interface condition is derived by imposing the given boundary condition weakly with the penalty parameter as in the Nitsche trick and it maintains ellipticity. Then, the derived interface problems can be solved by the hybrid difference approach together with a proper virtual to real transformation. Therefore, the boundary value problems can be solved on a fixed mesh independently of geometric shapes of boundaries. Numerical tests on several types of boundary interfaces are presented to demonstrate efficiency of the suggested method.
- Artificial interface condition,
- elliptic boundary value problem,
- immersed hybrid difference,
- VR transformation
Citation: Youngmok Jeon, Dongwook Shin. Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions[J]. Electronic Research Archive, 2021, 29(5): 3361-3382. doi: 10.3934/era.2021043

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Abstract

We propose an immersed hybrid difference method for elliptic boundary value problems by artificial interface conditions. The artificial interface condition is derived by imposing the given boundary condition weakly with the penalty parameter as in the Nitsche trick and it maintains ellipticity. Then, the derived interface problems can be solved by the hybrid difference approach together with a proper virtual to real transformation. Therefore, the boundary value problems can be solved on a fixed mesh independently of geometric shapes of boundaries. Numerical tests on several types of boundary interfaces are presented to demonstrate efficiency of the suggested method.

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