We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse estimate which allows us to prove the stability of the finite element method under practical interface resolving mesh conditions and also prove the lower bound of the hp a posteriori error estimate. Numerical examples are included.
翻译:我们设计了一种适应性不适的有限元素方法,用挂接节点在笛卡尔网格上。我们从K-meshes的事后误差估计中得出一种 hp 可靠和高效的剩余类型。一个关键成分是新颖的 hp-dus 域反向估计,它使我们能够在解决网格条件的实际界面下证明有限元素方法的稳定性,并证明hp 后端误差估计的下限。其中列举了数字实例。