Zobrazeno 1 - 10
of 179
pro vyhledávání: '"Xenophontos, Christos A."'
We prove deep neural network (DNN for short) expressivity rate bounds for solution sets of a model class of singularly perturbed, elliptic two-point boundary value problems, in Sobolev norms, on the bounded interval $(-1,1)$. We assume that the given
Externí odkaz:
http://arxiv.org/abs/2401.06656
Autor:
Linß, Torsten, Xenophontos, Christos
We establish robust exponential convergence for $rp$-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{balanced norm} which is stronger than the usual energy norm associated with the proble
Externí odkaz:
http://arxiv.org/abs/2309.10387
Autor:
Linß, Torsten, Xenophontos, Christos
We present the analysis for an $hp$ weak Galerkin-FEM for singularly perturbed reaction-convection-diffusion problems in one-dimension. Under the analyticity of the data assumption, we establish robust exponential convergence, when the error is measu
Externí odkaz:
http://arxiv.org/abs/2211.04224
Autor:
Xenophontos, Christos
As the title suggests, we give a formula for the $n^{th}$ derivative of a quotient of two functions, analogous to Leibniz's formula for the product. This particular note has remained unpublished since 2007 (available only my website), however it has
Externí odkaz:
http://arxiv.org/abs/2110.09292
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree $p\geq 3$
Externí odkaz:
http://arxiv.org/abs/2107.06553
Autor:
Linß, Torsten, Xenophontos, Christos
Publikováno v:
In Computers and Mathematics with Applications 15 June 2024 164:95-103
Autor:
Linß, Torsten, Xenophontos, Christos
Publikováno v:
In Applied Numerical Mathematics March 2024 197:1-14
We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called {\emph{Sp
Externí odkaz:
http://arxiv.org/abs/1909.01243
We consider a second order, two-point, singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and we obtain regularity results for its solution. First we establish classical differentiability bou
Externí odkaz:
http://arxiv.org/abs/1901.09397
Autor:
Liotati, Klio, Xenophontos, Christos
We perform numerical experiments on one-dimensional singularly perturbed problems of reaction-convection-diffusion type, using isogeometric analysis. In particular, we use a Galerkin formulation with B-splines as basis functions. The question we addr
Externí odkaz:
http://arxiv.org/abs/1901.01949