We propose an immersed hybrid difference method for elliptic boundary value problems by artificial interface conditions. The artificial in-terface 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
2020 Mathematics Subject Classification. Primary: 65L12, 65N06, 65N50. Key words and phrases. Artificial interface condition, elliptic boundary value problem, immersed hybrid difference, VR transformation. Jeon was supported by NRF 2018R1D1A1A09082082 and Shin was supported by 2020 Research Fund of Myongji University. \u2217 Corresponding author.
