Immersed Hybrid Difference Methods For Elliptic Boundary Value Problems By Artificial Interface Conditions - Jeon, Youngmok; Shin, Dongwook (Electronic Research Archive, 2021)
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
Keywords: Artificial interface condition; elliptic boundary value problem; immersed hybrid difference; VR transformation