### Electronic Research Archive

2021, 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

• 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.

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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• 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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