论文标题
在修剪几何形状上的stokes问题的等因几何分散
Isogeometric discretizations of the Stokes problem on trimmed geometries
论文作者
论文摘要
研究了修剪域中的Stokes问题的等几何近似。该设置的特征是一个基本网状，与物理领域的边界未固定，使基本边界条件成为一个具有挑战性的问题。一个非常流行的策略是依靠所谓的Nitsche方法\ cite {MR3264337}。我们表明，Nitsche方法在某些退化的修剪域配置中缺乏稳定性，可能会污染计算的解决方案。在将\ cite {MR4155233}的稳定过程扩展到不可压缩的流问题之后，我们表明我们恢复了公式的良好性，因此，最佳的先验误差估计值。包括说明稳定性和收敛速率的数值实验。
The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary conditions a challenging problem. A very popular strategy is to rely on the so-called Nitsche method \cite{MR3264337}. We show that the Nitsche method lacks stability in some degenerate trimmed domain configurations, potentially polluting the computed solutions. After extending the stabilization procedure of \cite{MR4155233} to incompressible flow problems, we show that we recover the well-posedness of the formulation and, consequently, optimal a priori error estimates. Numerical experiments illustrating stability and converge rates are included.
