Browsing by Author "Xenophontos, Christos A."
Now showing items 21-40 of 47
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Article
hp finite element methods for fourth order singularly perturbed boundary value problems
Xenophontos, Christos A.; Melenk, M.; Madden, N.; Oberbroeckling, L.; Panaseti, Pandelitsa; Zouvani, A. (2013)We consider fourth order singularly perturbed boundary value problems (BVPs) in one-dimension and the approximation of their solution by the hp version of the Finite Element Method (FEM). If the given problem's boundary ...
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Article
An hp-fem for singularly perturbed transmission problems
Nicaise, S.; Xenophontos, Christos A. (2017)We perform the analysis of the hp finite element approximation for the solution to singularly perturbed transmission problems, using Spectral Boundary Layer Meshes. In [12] it was shown that this method yields robust ...
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Article
A note on p/hp finite element methods for reaction-diffusion problems in polygonal domains
Xenophontos, Christos A. (2000)We present guidelines on how to choose the mesh and polynomial degree distribution for the approximation of reaction-diffusion problems in polygonal domains, in the context of the hp finite element method. These guidelines ...
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Article
A note on the convergence rate of the finite element method for singularly perturbed problems using the Shishkin mesh
Xenophontos, Christos A. (2003)We consider the numerical approximation of singularly perturbed problems by the h version of the finite element method on a piecewise uniform, Shishkin mesh. It is well known that this method yields uniform approximations, ...
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Article
Numerical analysis meets number theory: Using rootfinding methods to calculate inverses mod pn
Knapp, M. P.; Xenophontos, Christos A. (2010)We show how classical rootfinding methods from numerical analysis can be used to calculate inverses of units modulo prime powers.
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Article
A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems
Xenophontos, Christos A.; Oberbroeckling, L. (2007)We consider the approximation of singularly perturbed systems of reaction-diffusion problems, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the ...
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Article
On the effects of using curved elements in the approximation of the Reissner-Mindlin plate by the p version of the finite element method
Kurtz, J.; Xenophontos, Christos A. (2003)We consider the approximation of the Reissner-Mindlin plate model by the standard Galerkin p version finite element method. Under the assumption of sufficient smoothness on the solution, we illustrate that the method is ...
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Article
On the finite element approximation of systems of reaction-diffusion equations by p/hp methods
Xenophontos, Christos A.; Oberbroeckling, L. (2010)We consider the approximation of systems of reaction-diffusion equations, with the finite element method. The highest derivative in each equation is multiplied by a parameter ε∈ G (0,1], and as ε → 0 the solution of the ...
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Article
Optimal mesh design for the finite element approximation of reaction-diffusion problems
Xenophontos, Christos A. (2002)We consider the numerical approximation of singularly perturbed problems, and in particular reactiondiffusion problems, by the h version of the finite element method. We present guidelines on how to design non-uniform ...
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Article
A p-version MITC finite element method for Reissner-Mindlin plates with curved boundaries
Xenophontos, Christos A.; Kurtz, J.; Fulton, S. (2006)We consider the approximation of Reissner-Mindlin plates with curved boundaries, using a p-version MITC finite element method. We describe in detail the formulation and implementation of the method, and emphasize the need ...
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Article
A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems
Xenophontos, Christos A. (2017)We consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ...
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Article
A PILOT STUDY IN NON‐CONTACT LASER PHOTOTHERMAL ARCHAEOMETRY OF ANCIENT STATUARY PEDESTAL STONES FROM CYPRUS
Mandelis, Andreas; McALLISTER, K.; Christofides, Constantinos; Xenophontos, Christos A. (1995)
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Article
Robust approximation of singularly perturbed delay differential equations by the hp finite element method
Nicaise, S.; Xenophontos, Christos A. (2013)We consider the finite element approximation of the solution to a singularly perturbed second order differential equation with a constant delay. The boundary value problem can be cast as a singularly perturbed transmission ...
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Article
Robust exponential convergence of hp FEM for singularly perturbed reaction-diffusion systems with multiple scales
Melenk, J. M.; Xenophontos, Christos A.; Oberbroeckling, L. (2013)We consider a coupled system of two singularly perturbed reaction-diffusion equations in one dimension. Associated with the two singular perturbation parameters 0 < ε ≤ μ ≤ 1 are boundary layers of length scales O(ε) and ...
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Article
Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion equations
Melenk, J. M.; Xenophontos, Christos A. (2016)The hp-version of the finite element method is applied to a singularly perturbed reaction-diffusion equation posed on an interval or a two-dimensional domain with an analytic boundary. On suitably designed Spectral Boundary ...
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Article
The singular function boundary integral method for 3-D Laplacian problems with a boundary straight edge singularity
Christodoulou, Evgenia; Elliotis, Miltiades C.; Xenophontos, Christos A.; Georgiou, Georgios C. (2012)Three-dimensional Laplace problems with a boundary straight-edge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...
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Article
The singular function boundary integral method for a two-dimensional fracture problem
Elliotis, Miltiades C.; Georgiou, Georgios C.; Xenophontos, Christos A. (2006)The singular function boundary integral method (SFBIM) originally developed for Laplacian problems with boundary singularities is extended for solving two-dimensional fracture problems formulated in terms of the Airy stress ...
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Article
The singular function boundary integral method for biharmonic problems with crack singularities
Elliotis, Miltiades C.; Georgiou, Georgios C.; Xenophontos, Christos A. (2007)We use the singular function boundary integral method (SFBIM) to solve two model fracture problems on the plane. In the SFBIM, the solution is approximated by the leading terms of the local asymptotic solution expansion, ...
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Article
A singular function boundary integral method for laplacian problems with boundary singularities
Xenophontos, Christos A.; Elliotis, Miltiades C.; Georqiou, Georgios E. (2006)A singular function boundary integral method for Laplacian problems with boundary singularities is analyzed. In this method, the solution is approximated by the truncated asymptotic expansion for the solution near the ...
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Conference Object
The singular function boundary integral method for Laplacian problems with boundary singularities in two and three-dimensions
Xenophontos, Christos A.; Christodoulou, Evgenia; Georgiou, Georgios C. (2010)We present a Singular Function Boundary Integral Method (SFBIM) for solving elliptic problems with a boundary singularity. In this method the solution is approximated by the leading terms of the asymptotic solution expansion, ...