A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations 32 2007, 7–9, 1345–1371], that the disk will never touch the boundary of the domain in finite time. Anisotropic, continuous piecewise linear finite elements are used for the space discretization, the Euler scheme for the time discretization. The adaptive criteria are based on a posteriori error estimates for simpler problems.

中文翻译：

---

时空自适应算法来说明硬盘碰撞时落在不可压缩流体中的缺乏

提出了一种时空自适应算法来解决刚性磁盘在不可压缩牛顿流体中的运动，该算法可以高精度地计算碰撞或准碰撞过程。特别是，我们恢复了在[M. Hillairet，《二维不可压缩粘性流中的实体之间缺乏碰撞》，Comm。偏微分方程32 2007，7–9，1345–1371]，表明磁盘将在有限时间内永远不会接触域的边界。各向异性的，连续的分段线性有限元用于空间离散化，而Euler方案用于时间离散化。自适应准则基于后验误差估计，用于更简单的问题。