High-dimensional Collocation Weighted Approximations For Parametric Elliptic PDEs With Lognormal Inputs


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Authors

  • Dinh D˜ung Information Technology Institute, Vietnam National University

Keywords:

High-dimensional approximation, parametric and stochastic elliptic PDEs, lognormal inputs, collocation method, non-adaptive weighted polynomial interpolation approximation

Abstract

We constructed linear non-adaptive methods of non-fully and fully discrete polynomial interpolation weighted approximation for parametric and stochastic elliptic PDEs with
lognormal inputs and proved convergence rates of the approximations by them. Our methods are
sparse-grid collocation methods. Moreover, the fully discrete methods can be seen as multilevel
methods of approximation. The Smolyak sparse interpolation grids in the parametric domain
are constructed from the roots of Hermite polynomials or their improved modifications.

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Published

2019-06-30

How to Cite

Динь Зунг. (2019). High-dimensional Collocation Weighted Approximations For Parametric Elliptic PDEs With Lognormal Inputs. Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, Computer Science, Mechanics Series, 127(2), 39–45. Retrieved from https://bulmathmc.enu.kz/index.php/main/article/view/48

Issue

Vol. 127 No. 2 (2019)

Section

Статьи