论文标题
用于椭圆界面问题的自适应高阶未有限元方法
An adaptive high-order unfitted finite element method for elliptic interface problems
论文作者
论文摘要
我们在带有悬挂节点的笛卡尔网格上设计了一种自适应的未有限元方法。我们在K-MESHES上得出了HP可信和有效的剩余A后验错误估计。一个关键成分是一种新型的HP域反估计，它使我们能够在解决网格条件下证明有限元方法的稳定性，并证明HP的下限A后验误差估计值。包括数值示例。
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.
