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The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting.
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2017
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M. D’Elia, Q. Du, M. Gunzburger, and R. Lehoucq, Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes , Computational Methods in Applied Mathematics 17
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M. Ainsworth and C. Glusa, Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains , Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan, Springer, 2018, pp. 17–57
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2019
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C. Vollmann, Nonlocal models with truncated interaction kernels - analysis, finite element methods and shape optimization , Doctoral Thesis, Universität Trier, 2019
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2020
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M. D’Elia, X. Tian, and Y. Yu, A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraints , Accepted for publication in SIAM Journal of Scientific Computing
2020
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A. Lischke, G. Pang, M. Gulian, F. Song, C. Glusa, X. Zheng, Z. Mao, W. Cai, M. M. Meerschaert, M. Ainsworth, and G. E. Karniadakis, What is the fractional Laplacian? A comparative review with new results , Journal of Computational Physics 404
2020
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2020
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