40 citations · 59 across the 17 of their papers we have counts for
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A simple shallow neural network for emulating the solution to singularly perturbed problems
Christos Xenophontos, Aayushman Raina
We consider (feed-forward) Neural Networks (NNs) for the emulation of the solution to singularly perturbed second order boundary value problems, with two small parameters. We descr…
Analytic regularity for a fourth-order singularly perturbed boundary balue problem with two small parameters
I. Sykopetritou, C. Xenophontos
We consider a fourth order singularly perturbed boundary value problem with two small parameters, in one dimension, under the assumption of analytic input data. We show that the so…
Neural Networks for Singular Perturbations -- Finite Regularity
F. Rohner, Ch. Schwab, C. Xenophontos
We study finite-element and deep feedforward neural network (DNN for short) expressivity rate bounds for solution sets of a model linear, second order singularly perturbed, ellipti…
On norms and traces of the derivatives of the -projection error
Torsten Linß, Christos Xenophontos
We provide error bounds on the traces and norms of the derivative of the projection of an function onto the space of polynomials of degree . The bounds are ex…
Neural Networks for Singular Perturbations
Joost A. A. Opschoor, Christoph Schwab, Christos Xenophontos
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 Sob…
Balanced norm estimates for -Finite Element Methods applied to singularly perturbed fourth order boundary value problems
Torsten Linß, Christos Xenophontos
We establish robust exponential convergence for -Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{balanced norm} w…
An Weak Galerkin FEM for singularly perturbed problems
Torsten Linß, Christos Xenophontos
We present the analysis for an weak Galerkin-FEM for singularly perturbed reaction-convection-diffusion problems in one-dimension. Under the analyticity of the data assumption…
On the finite element approximation of fourth order singularly perturbed eigenvalue problems
Hans-Görg Roos, Despo Savvidou, Christos Xenophontos
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the version of the Finite Element Method (FEM). In…
Mixed FEM for singularly perturbed fourth order boundary value problems with two small parameters
C. Xenophontos, S. Franz, I. Sykopetritou
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the version of the Finite Element M…
Isogeometric Analysis for singularly perturbed problems in 1-D: a numerical study
Klio Liotati, Christos Xenophontos
We perform numerical experiments on one-dimensional singularly perturbed problems of reaction-convection-diffusion type, using isogeometric analysis. In particular, we use a Galerk…
On a connection between layer-adapted exponentially graded and S-type meshes
Sebastian Franz, Christos Xenophontos
In this short note we analyse a connection between the exponentially graded and the class of S-type meshes for singularly perturbed problems. As a by-product we obtain a slightly m…
Robust exponential convergence of -FEM in balanced norms for singularly perturbed reaction-diffusion equations
Jens Markus Melenk, Christos Xenophontos
The -version of the finite element method is applied to a singularly perturbed reaction-diffusion equation posed in one- and two-dimensional domains with analytic boundary. On…
Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs
Jens Markus Melenk, Christos Xenophontos, Lisa Oberbroeckling
We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters , each multiplying the highest derivative in the eq…