This paper proposes an interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method for Darcy-Stokes-Brinkman interface problems in two and three dimensions. The method uses piecewise linear polynomials for the velocity approximation and piecewise constants for both the velocity gradient and pressure approximations in the interior of elements inside the subdomains separated by the interface, uses piecewise constants for the numerical traces of velocity on the inter-element boundaries inside the subdomains, and uses piecewise constants or linear polynomials for the numerical traces of velocity on the interface. Optimal error estimates are derived for the interface-unfitted X-HDG scheme. Numerical experiments are provided to verify the theoretical results and the robustness of the proposed method.

翻译：本文为达西-斯托克斯-布林克曼接口问题提出了两个和三个维度的界面/边际可混合不相干加勒金(X-HDG)方法。该方法使用节奏线性线性多边近似和片度常数来计算由接口分离的子域内各元素内部的速度梯度和压力近似,使用节奏常数来计算子域内各元素间界间速度的数字微量,并使用片断常数或线性多式来计算界面上速度的数字微量。为接口不相配的 X-HDG 方案得出了最佳误差估计。提供了数字性实验,以核实拟议方法的理论结果和稳健性。