论文标题
部分可观测时空混沌系统的无模型预测
Well-Posedness and Finite Element Approximation of Mixed Dimensional Partial Differential Equations
论文作者
论文摘要
我们考虑在具有大量嵌入式接口的散装结构域中构成的混合尺寸椭圆偏微分方程。特别是，我们研究了解决方案的问题和规律性。我们还提出了一个拟合的有限元近似值，并证明了一个先验误差。对于出现的线性系统的解决方案，我们建议并分析基于子空间分解的迭代方法。最后，我们提出了数值实验，并使用拟议的预定器实现快速收敛，从而确认了我们的理论发现。
We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose a fitted finite element approximation and prove an a priori error bound. For the solution of the arising linear system we propose and analyze an iterative method based on subspace decomposition. Finally, we present numerical experiments and achieve rapid convergence using the proposed preconditioner, confirming our theoretical findings.
