AI 中文总结
本文针对边界可任意切割计算网格的双调和Dirichlet问题，提出带最小二乘稳定化Nitsche边界条件的CutIGA方法，分析其误差界并通过精确椭圆实验验证收敛性等特性。
AI 中文摘要
针对边界可任意切割计算网格的光滑区域上的双调和Dirichlet问题，我们提出了一种对称Nitsche方法。边界带内的体最小二乘稳定化以及切向边界罚项，通过对两个Dirichlet迹线的显式提升来控制一致性项，这在不使用逆不等式的情况下为$H^4(\Omega)$提供了强制性，且对于足够薄的边界带，允许采用与切割构型无关的固定罚项。在适当正则性假设下，次数$p\geq4$的样条给出能量和$L^2$误差界，阶数分别为$h^{p-1}$和$h^{p+1}$。我们还分析了面向$C^1$次数$p=2$样条和$C^2$次数$p=3$样条的面稳定化扩展。精确椭圆实验检验了收敛性、切割稳定性和参数敏感性。
英文摘要
We propose a symmetric Nitsche method for the biharmonic Dirichlet problem on a smooth domain whose boundary may cut arbitrarily through the computational mesh. Bulk least-squares stabilization in a boundary strip and tangential boundary penalties control the consistency terms through an explicit lifting of the two Dirichlet traces. This gives coercivity on $H^4(Ω)$ without inverse inequalities and permits a fixed penalty independent of the cut configuration for sufficiently thin strips. Under suitable regularity assumptions, splines of degree $p\geq4$ give energy and $L^2$ error bounds of orders $h^{p-1}$ and $h^{p+1}$. We also analyze a face-stabilized extension to $C^1$ splines of degree $p=2$ and $C^2$ splines of degree $p=3$. Exact-ellipse experiments examine convergence, cut stability, and parameter sensitivity.
