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- W4287394580 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 $2delta$-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 2 specific numerical examples to illustrate the quadratic rate of convergence on the other side." @default.
- W4287394580 created "2022-07-25" @default.
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- W4287394580 date "2021-01-04" @default.
- W4287394580 modified "2023-09-23" @default.
- W4287394580 title "A Second-Order Nonlocal Approximation for Manifold Poisson Model with Dirichlet Boundary" @default.
- W4287394580 doi "https://doi.org/10.48550/arxiv.2101.01016" @default.
- W4287394580 hasPublicationYear "2021" @default.
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