Browsing 002 Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences by Author "Xenophontos, Christos A."
Now showing items 1-20 of 47
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Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity
Christodoulou, Evgenia; Elliotis, Miltiades C.; Georgiou, Georgios C.; Xenophontos, Christos A. (2012)In this article, we analyze the singular function boundary integral method (SFBIM) for a two-dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick-slip flow problem. In the SFBIM, ...
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Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales
Melenk, J. M.; Xenophontos, Christos A.; Oberbroeckling, L. (2013)We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters 0 < ε ≤ μ ≤ 1, each multiplying the highest derivative in the equations. The presence of these parameters ...
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An analytical method for linear elliptic PDEs and its numerical implementation
Fulton, S. R.; Fokas, A. S.; Xenophontos, Christos A. (2004)A new numerical method for solving linear elliptic boundary value problems with constant coefficients in a polygonal domain is introduced. This method produces a generalized Dirichlet-Neumann map: given the derivative of ...
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Application of the p-version of the finite element method to elastoplasticity with localization of deformation
Jeremić, B.; Xenophontos, Christos A. (1999)In this paper we discuss the use of the p-version of the finite element method applied to elastoplastic problems that exhibit sharp (but continuous) deformation gradients. The deformation theory of deviatoric, linearly ...
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Article
A C1-conforming hp finite element method for fourth order singularly perturbed boundary value problems
Panaseti, Pandelitsa; Zouvani, A.; Madden, N.; Xenophontos, Christos A. (2016)We consider a fourth order singularly perturbed boundary value problem (BVP) in one-dimension and the approximation of its solution by the hp version of the Finite Element Method (FEM). The given problem's boundary conditions ...
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Cessation of annular Poiseuille flows of Bingham plastics
Chatzimina, Maria Evangelia; Xenophontos, Christos A.; Georgiou, Georgios C.; Argyropaidas, Ioannis; Mitsoulis, Evan C. (2007)We numerically solve the cessation of the annular Poiseuille flow of Bingham plastics for various values of the diameter ratio, using the regularized constitutive equation proposed by Papanastasiou and employing finite ...
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Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains
Nicaise, S.; Xenophontos, Christos A. (2013)We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of ...
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Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains
Nicaise, Serge; Xenophontos, Christos A. (2013)
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An enriched subspace finite element method for convection-diffusion problems
Kellogg, R. B.; Xenophontos, Christos A. (2010)We consider a one-dimensional convection-diffusion boundary value problem, whose solution contains a boundary layer at the outflow boundary, and construct a finite element method for its approximation. The finite element ...
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FFinite element approximation of convection–diffusion problems using an exponentially graded mesh
Xenophontos, Christos A.; Franz, Sebastian; Ludwig, Lars (2016)
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Finite element analysis of an exponentially graded mesh for singularly perturbed problems
Constantinou, P.; Xenophontos, Christos A. (2015)We present the mathematical analysis for the convergence of an h version Finite Element Method (FEM) with piecewise polynomials of degree p ≥ 1, defined on an exponentially graded mesh. The analysis is presented for a ...
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Article
Finite element approximation of convection–diffusion problems using an exponentially graded mesh
Xenophontos, Christos A.; Franz, S.; Ludwig, L. (2016)We present the analysis of an h version Finite Element Method for the approximation of the solution to convection–diffusion problems. The method uses piece-wise polynomials of degree p≥1, defined on an exponentially graded ...
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Finite element computations for the Reissner-Mindlin plate model
Xenophontos, Christos A. (1998)We consider the finite element (FE) approximation of the Reissner - Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p/hp version of the standard FE method is used. These ...
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Article
Finite element methods for a singularly perturbed transmission problem
Nicaise, S.; Xenophontos, Christos A. (2009)We consider a one-dimensional singularly perturbed transmission problem with two different diffusion coefficients. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient ...
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Article
An hp finite element method for 4th order singularly perturbed problems
Constantinou, P.; Varnava, C.; Xenophontos, Christos A. (2016)We present the analysis for the hp finite element approximation of the solution to singularly perturbed fourth order problems, using a balanced norm. In Panaseti et al. (2016) it was shown that the hp version of the Finite ...
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An hp finite element method for a 4th order singularly perturbed boundary value problem in two dimensions
Constantinou, P.; Xenophontos, Christos A. (2017)We consider a fourth order singularly perturbed boundary value problem posed in a square and the approximation of its solution by the hp version of the finite element method on the so-called Spectral Boundary Layer mesh. ...
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The hp finite element method for problems in mechanics with boundary layers
Schwab, C.; Suri, M.; Xenophontos, Christos A. (1998)Boundary layer phenomena are well-known in the study of fluid flow problems. Perhaps less known, but equally ubiquitous, is their existence in thermal, plate and shell analysis, where they also play a very significant role. ...
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The hp finite element method for singularly perturbed problems in nonsmooth domains
Xenophontos, Christos A. (1999)We consider the numerical approximation of singularly perturbed elliptic boundary value problems over nonsmooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary ...
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The hp finite element method for singularly perturbed problems in smooth domains
Xenophontos, Christos A. (1998)We consider the numerical approximation of singularly perturbed elliptic problems in smooth domains. The solution to such problems can be decomposed into a smooth part and a boundary layer part. We present guidelines for ...
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The hp finite element method for singularly perturbed systems of reaction-diffusion equations
Xenophontos, Christos A. (2008)We consider the approximation of a coupled system of two singularly perturbed reaction-diffusion equations, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, ...