High order immersed hybridized difference methods for elliptic interface problems

Abstract

We propose high order conforming and nonconforming immersed hybridized difference (IHD) methods in two and three dimensions for elliptic interface problems. Introducing the virtual to real transformation (VRT), we could obtain a systematic and unique way of deriving arbitrary high order methods in principle. The optimal number of collocating points for imposing interface conditions is proved, and a unique way of constructing the VRT is suggested. Numerical experiments are performed in two and three dimensions. Numerical results achieving up to the 6th order convergence in the L2-norm are presented for the two dimensional case, and a three dimensional example with a 4th order convergence is presented.