论文标题
低规律性估计值的椭圆形问题的CutFem近似值混合边界条件
Low Regularity Estimates for CutFEM Approximations of an Elliptic Problem with Mixed Boundary Conditions
论文作者
论文摘要
我们显示了与混合边界条件的二阶椭圆问题的切割有限元近似值的错误估计。误差估计值是低规律性类型的，在考虑情况下，当确切的解决方案$ u \ in h^s $带有$ s \ in（1,3/2] $。对数因素。
We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$ with $s\in (1,3/2]$. For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.
