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Vortrag: "Radial discrete PDE splines"

Joaquín Jódar Reyes (Uni Jaen, Spanien)

Wann

07.09.2017 von 12:15 bis 14:15 (Europe/Berlin / UTC200)

Wo

Seminarraum 32, EG, Mathem. Institut, Arndtstr. 2

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Abstract:

Radial basis function (RBF) methods have emerged as an important and effective tool for the numerical solution of partial differential equations
(PDE) in any number of dimensions and for the approximation of an unknown multivariate function by interpolation at scattered sites, entering in a field traditionally tackled by finite element methods.

Also, PDE surfaces, which are surfaces whose behaviour is governed by PDE, have shown to possess many modeling advantages in a wide range of fields. A combination of conditions of interpolation and approximation can be regarded for the PDE method of surface design. Although the method is not confined to any particular type of PDE, mainly elliptic PDE have been used as they produce smooth surfaces for boundary value problems. Moreover, a generalization of the method to any dimension can be considered.

In the framework of a PDE, certain boundary conditions and a set of points to approximate in a Lipschitz domain and arbitrary dimension, we use in this talk RBF techniques for the construction and characterization of discrete PDE splines. We show convergence, we derive error estimates and, to illustrate, we also provide several numerical examples.