Asymptotically compatible schemes for robust discretization of nonlocal models and their local limit
【2014.1.8 10:00am,Z311】 |
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2014-01-06
Colloquia & Seminars
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Speaker |
Prof.Qiang Du，Pennsylvania State University, and Beijing Computational Science Research Center |
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Title |
Asymptotically compatible schemes for robust discretization of nonlocal models and their local limit |
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Time |
2014.1.8 10:00am |
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Venue |
Z311 |
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Abstract |
We present an abstract framework of asymptotically compatiable (AC) schemes for robust discretizations of a family of parametrized problems. The AC schemes provide convergent approximations to problems associated with fixed parameter values as well as their limiting values. This framework is then applied to study approximations of nonlocal models such as peridynamic models of nonlocal elasticity parametrzed by the horizon parameter and their local PDE limits (Navier equations) when the horizon parameter approaches zero. In particular, by combining with the theory of nonlocal calculus of variations, a precise characterization of AC schemes can be obtained for popular conforming finite element discretizations. |
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Affiliation |
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