论文标题
部分可观测时空混沌系统的无模型预测
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
论文作者
论文摘要
我们引入了一种数学上严格的公式，以解决跳跃的非本地界面问题，并提出了涉及接口问题的弱形式的渐近兼容有限元离散化。在证明了弱形式的适当性之后，我们证明了在适当规定非局部数据时，非本地界面问题的解决方案会收敛到相应的本地对应物。一个和二维中的几个数值测试显示了我们技术的适用性，其数值收敛到确切的非局部溶液，当地平线消失时，其收敛到局部极限以及相对于斑块测试的稳健性。
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test.
