Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Author "Xenophontos, Christos A."
Now showing items 120 of 46

Article
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 twodimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stickslip flow problem. In the SFBIM, ...

Article
Analytic regularity for a singularly perturbed system of reactiondiffusion equations with multiple scales
Melenk, J. M.; Xenophontos, Christos A.; Oberbroeckling, L. (2013)We consider a coupled system of two singularly perturbed reactiondiffusion equations, with two small parameters 0 < ε ≤ μ ≤ 1, each multiplying the highest derivative in the equations. The presence of these parameters ...

Article
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 DirichletNeumann map: given the derivative of ...

Article
Application of the pversion 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 pversion of the finite element method applied to elastoplastic problems that exhibit sharp (but continuous) deformation gradients. The deformation theory of deviatoric, linearly ...

Article
A C1conforming 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 onedimension and the approximation of its solution by the hp version of the Finite Element Method (FEM). The given problem's boundary conditions ...

Article
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 ...

Article
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 twodimensional 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 ...

Article
Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains
Nicaise, Serge; Xenophontos, Christos A. (2013)

Article
An enriched subspace finite element method for convectiondiffusion problems
Kellogg, R. B.; Xenophontos, Christos A. (2010)We consider a onedimensional convectiondiffusion 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 ...

Article
FFinite element approximation of convection–diffusion problems using an exponentially graded mesh
Xenophontos, Christos A.; Franz, Sebastian; Ludwig, Lars (2016)

Article
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 ...

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 piecewise polynomials of degree p≥1, defined on an exponentially graded ...

Article
Finite element computations for the ReissnerMindlin 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 ...

Article
Finite element methods for a singularly perturbed transmission problem
Nicaise, S.; Xenophontos, Christos A. (2009)We consider a onedimensional 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 ...

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 ...

Article
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 socalled Spectral Boundary Layer mesh. ...

Article
The hp finite element method for problems in mechanics with boundary layers
Schwab, C.; Suri, M.; Xenophontos, Christos A. (1998)Boundary layer phenomena are wellknown 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. ...

Article
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 ...

Article
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 ...

Article
The hp finite element method for singularly perturbed systems of reactiondiffusion equations
Xenophontos, Christos A. (2008)We consider the approximation of a coupled system of two singularly perturbed reactiondiffusion equations, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, ...