Seminar| Institute of Mathematical Sciences
Time：Friday, March 24th, 2023, 15:00-16:00
Location：RS408, IMS
Speaker: Yajie Zhang, Zhongnan University of Economics and Law
Abstract: Recently, we constructed a class of nonlocal Poisson model on manifold under Dirichlet boundary with global $\mathcal{O}(\delta^2)$ truncation error to its local counterpart, where $\delta$ denotes the nonlocal horizon parameter. In this paper, the well-posedness of such manifold model is studied. We utilize Poincare inequality to control the lower order terms along the $2\delta$-boundary layer in the weak formulation of model.
The second order localization rate of model is attained by combining the well-posedness argument and the truncation error analysis. Such rate is currently optimal among all nonlocal models. Besides, we implement the point integral method(PIM) to our nonlocal model through 4 specific numerical examples to illustrate the quadratic rate of convergence on the other side.