Extrinsic Meshless Collocation Methods for PDEs on Manifolds
نویسندگان
چکیده
منابع مشابه
Stable and Convergent Unsymmetric Meshless Collocation Methods
In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...
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Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...
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A central problem of numerical analysis is the approximate evaluation of integrals or derivatives of functions. In more generality, this is the approximate evaluation of a linear functional defined on a space of functions. Users often just have values of a function u at scattered points x1, . . . ,xN in the domain Ω of u, and then the value λ (u) of a linear functional λ must be approximated vi...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2020
ISSN: 0036-1429,1095-7170
DOI: 10.1137/17m1158641