In the present work, we examine and analyze an alternative of the unfitted mesh finite element method improved by omitting computationally expensive, especially for fluids, stabilization type of penalty onto the boundary area, namely the so-called ghost penalty. This approach is based on the discontinuous Galerkin method, enriched by arbitrarily shaped boundary elements techniques. In this framework, we examine a stationary Stokes fluid system and we prove the inf/sup condition, the hp- a priori error estimates, to our knowledge for the first time in the literature, while we investigate the optimal convergence rates numerically. This approach recovers and integrates the flexibility and superiority of the unfitted methods whenever geometrical deformations are taking place, combined with the efficiency of the hp-version techniques based on arbitrarily shaped elements on the boundary.

翻译：本文研究并分析了一种无拟合网格有限元方法的替代方案，该方案通过省略计算成本高昂的（尤其对于流体而言）边界惩罚稳定化项（即所谓的“幽灵惩罚”）而得以改进。该方法基于间断伽辽金法，并融合了任意形状边界单元技术。在此框架下，我们考察了稳态Stokes流体系统，首次在文献中证明了inf-sup条件及hp-先验误差估计，同时通过数值实验研究了最优收敛速度。该方法在几何变形发生时，恢复并整合了无拟合方法的灵活性与优越性，并结合了基于边界上任意形状单元的hp-版本技术的效率。