PUBLICATIONS

(Including Conference Proceedings and Technical Reports)


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JOURNAL ARTICLES PROCEEDINGS TECHNICAL REPORTS OTHER

Journal Artiles
M. J. Melenk and C. Xenophontos, Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion equations, submitted (2014).
P. Constantinou and C. Xenophontos, Finite element analysis of an exponentially graded mesh for singularly perturbed problems, submitted (2014).
P. Panaseti, A. Zouvani, N. Madden and C. Xenophontos, A C1-conforming hp Finite Element Method for fourth order singularly perturbed boundary value problems, accepted for publication in Applied Numerical Mathematics (2014).
S. Nicaise and C. Xenophontos, Convergence analysis of an hp Finite Element Method for singularly perturbed transmission problems in smooth domains, Numerical Methods for PDEs Vol. 29, Issue 6, pp. 2107 - 2132 (2013). (Journal link , PDF file.)
M. J. Melenk, C. Xenophontos and L. Oberbroeckling, Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales, Advances in Computational Mathematics, Vol. 39, pp. 367 - 394 (2013). (PDF file.)
S. Nicaise and C. Xenophontos, Robust approximation of singularly perturbed delay differential equations by the hp finite element method, Comp. Meth. Appl. Math., Vol. 13, pp. 21 - 37 (2013). (Journal link , PDF file.)
M. J. Melenk, C. Xenophontos and L. Oberbroeckling, Robust exponential convergence of hp-FEM for singularly perturbed systems of reaction-diffusion equations with multiple scales, IMA J. Num. Anal., Vol. 33., No 2, pp. 609 - 628, (2013) doi: 10.1093/imanum/drs013. (PDF file.)
E. Christodoulou, M. Elliotis, C. Xenophontos and G. Georgiou, The Singular Function Boundary Integral Method for 3-D Laplacian problems with a boundary straight edge singularity, Appl. Math. Comp., Vol. 219, pp. 1073 - 1081 (2012). (PDF file.)
E. Christodoulou, M. Elliotis, C. Xenophontos and G. Georgiou, Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity, Numer. Meth. PDEs, Vol. 28, No 3, pp 749 767 (2012). (PDF file.)
E. Christodoulou, C. Xenophontos and G. Georgiou, The Singular Function Boundary Integral Method for singular Laplacian problems over circular sectors, Applied Mathematics and Computation, Vol. 217, No. 5, pp. 2773 - 2787 (2010). (PDF file.)
M. Elliotis, E. Christodoulou, G. Georgiou and C. Xenophontos, The Singular Function Boundary Integral Method for a 3-D Laplacian problem with an edge singularity, Recent Developments in Boundary Element Methods (A Volume to honor Prof. Katsikadelis), pp. 31 - 42, WIT Press (2010).
M. Knapp and C. Xenophontos, Numerical analysis meets number theory: using root finding methods to calculate inverses mod pn, Applicable Analysis and Discrete Mathematics, Vol. 4, pp. 23 - 31 (2010). (PDF file.)
R. B. Kellogg and C. Xenophontos, An enriched subspace finite element method for convection-diffusion problems, International Journal of Numerical Analysis and Modeling, Vol. 7, No. 3, pp. 477 - 490 (2010). (PDF file.)
C. Xenophontos and L. Oberbroeckling, On the finite element approximation of systems of reaction-diffusion equations by p/hp methods, Journal of Computational Mathematics, Vol. 28, No. 3, pp. 386 - 400 (2010). (PDF file.)
S. Nicaise and C. Xenophontos, Finite element methods for a singularly perturbed transmission problem, Journal of Numerical Mathematics, Vol. 17, No. 4, pp. 245 - 275 (2009). (PDF file.)
E. Christodoulou, C. Xenophontos and G. Georgiou, The singular function boundary integral method for elliptic problems with boundary singularities, Recent Advances in Boundary Element Methods: A Volume to honor Prof. D. Beskos, G. Manolis and D. Polyzos (Eds), pp. 43 - 56, Springer-Verlag, 2009.
C. Xenophontos, The hp finite element approximation for singularly perturbed systems of reaction-diffusion equations, J. of Neural, Parallel and Scientific Computation (Special Issue on Singularly Perturbed Problems) Vol. 16, pp. 337 - 352 (2008).
M. Elliotis, G. Georgiou and C. Xenophontos, The singular function boundary integral method for biharmonic problems with crack singularities, Engineering Analysis with Boundary Elements, Vol 31, No. 3, pp 209 - 215 (2007). (PDF file.)
M. Chatzimina, C. Xenophontos, G. Georgiou, I. Argyropaidas and E. Mitsoulis, Cessation of annular Poiseuille flows of a Bingham plastic, J. Non-Newtonian Fluid Mechanics, Vol 142, pp. 135 - 142 (2007). (PDF file.)
C. Xenophontos and L. Oberbroeckling, A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems, Applied Mathematics and Computation, Vol. 187, pp. 1351 - 1367 (2007). (PDF file.)
C. Xenophontos, The use of curved elements in the finite element approximation of thin plates by high order p and hp methods, J. Scientific Computing, Vol. 27, pp. 465 - 476 (2006). (PDF file.)
C. Xenophontos, M. Elliotis and G. Georgiou The singular function boundary integral method for elliptic problems with singularities, SIAM Journal of Scientific Computing, Vol. 28, No 2., pp. 517 - 532 (2006). (PDF file.)
C. Xenophontos, J. Kurtz and S. R. Fulton, A p-version MITC finite element method for Reissner-Mindlin plates with smooth boundaries, Journal of Computational and Applied Mathematics, Vol. 192, No. 2, pp. 374 - 395 (2006). (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, The singular function boundary integral method for a two-dimensional fracture problem, Engineering Analysis with Boundary Elements, Vol. 30 , pp. 100 - 106 (2006). (PDF file.)
Z. C. Li, Y. L. Chen, G. Georgiou and C. Xenophontos, Special boundary approximation methods for Laplace equation problems with boundary singularities, Computers and Mathematics with Applications, Vol. 51, pp. 115 - 142 (2006). (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, Solution of the planar Newtonian stick-slip problem with the singular function boundary integral method, Int. J. Numer. Meth. Fluids, Vol. 48, pp. 1001 - 1021 (2005). (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, Solving Laplacian problems with boundary singularities: A comparison of a singular function boundary integral method with the p/hp version of the finite element method, Applied Mathematics and Computation, Vol. 169, No. 1, pp. 485-499 (2005). (PDF file.)
S. R. Fulton, A. S. Fokas and C. Xenophontos, An analytical method for linear elliptic PDEs and its numerical implementation, Journal of Computational and Applied Mathematics, Vol. 167, No. 2 , pp. 465-483 (2004). (PDF file.)
J. Kurtz and C. Xenophontos, On the effects of using curved elements in the approximation of the Reissner-Mindlin plate by the p version of the finite element method, Applied Numerical Mathematics, Vol. 46, No, 2, pp. 231-246 (2003). (PDF file.)
C. Xenophontos, A note on the convergence of the finite element method for singularly perturbed problems using the Shishkin mesh, Applied Mathematics and Computation, Vol. 42, No. 2/3, pp. 545 - 559 (2003). (PDF file.)
C. Xenophontos and S. R. Fulton, Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh, Numerical Methods for Partial Differential Equations, Vol. 19, No. 1, pp. 89 - 111 (2002) (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, The solution of Laplacian problems over L-shaped domains with a singular function boundary integral method, Communications in Numerical Methods in Engineering, Vol. 18, No. 3, pp. 213 - 222 (2002) (PDF file.)
C. Xenophontos, Optimal mesh design for the finite element approximation of reaction-diffusion problems, International Journal of Numerical Methods in Engineering, Vol. 53, No 4, pp. 929 - 943 (2002) (PDF file.)
C. Xenophontos, A note on the application of p/hp finite element methods to reaction-diffusion problems in polygonal domains, Communications in Numerical Methods in Engineering, Vol 16, No 6, pp. 391 - 400 (2000) (PDF file.)
B. Jeremic and C. Xenophontos, Application of the p-version of the finite element method to elasto-plasticity with localization of deformation, Communications in Numerical Methods in Engineering, Vol. 15, No. 12, pp. 867 - 876 (1999) ( PDF file.)
C. Xenophontos, The hp finite element method for singularly perturbed problems in non-smooth domains, Numerical Methods for Partial Differential Equations, Vol 15, No 1, pp. 63 - 90 (1999) (PDF file.)
C. Xenophontos, Finite Element computations for the Reissner-Mindlin plate model, Communications in Numerical Methods in Engineering, Vol 14, No. 12, pp. 1119 - 1131 (1998) (PDF file.)
C. Schwab, M. Suri and C. Xenophontos, The hp finite element method for problems in mechanics with boundary layers, Computer Methods in Applied Mechanics and Engineering, Vol 57, No 3/4, pp. 311 - 334 (1998) (PDF file.)
C. Xenophontos,The hp finite element method for singularly perturbed problems in smooth domains, Mathematical Models and Methods in Applied Sciences, Vol 2, No. 8, pp. 299 - 326 (1998) (PDF file.)
C. Schwab, M. Suri and C. Xenophontos, Boundary Layer Approximation by Spectral / hp Methods, Houston Journal of Mathematics, Special Issue of ICOSAHOM '95 Conference, A. V. Ilin and L. R. Scott (Editors), pp. 501 - 508 (1996). (PDF file.)
C. R. Johnson and C. Xenophontos, Irreducibility and primitivity of Perron complements, Institute of Mathematics and its Applications, Vol. 56, Graph Theory and Sparse Matrix Computations, pp. 101 - 106, Springer-Verlag, 1993.

Conference Proceedings
C. Xenophontos, M. Melenk, N. Madden, L. Oberbroeckling, P. Panaseti and A. Zouvani, hp finite element methods for fourth order singularly perturbed boundary value problems, Lecture Notes in Computer Science, Vol. 8236, Springer-Verlag, pp. 532 - 539 (2013). (PDF file.)
C. Xenophontos, E. Christodoulou and G. Georgiou, The singular function boundary integral method for Laplacian problems with boundary singularities in two and three- dimensions, Procedia Computer Science, Vol. 1, Springer-Verlag, pp. 2583 - 2591 (2010). (PDF file.)
E. Christodoulou, C. Xenophontos and G. Georgiou, The singular function boundary integral method for singular Laplacian problems over circular sectors, Proc. of the 2nd South-East European Conference on Computational Mechanics, M. Papadrakakis, M. Kojic, V. Papadopoulos (Eds), Rhodes, Greece, 22 - 24 June (2009).
M. Elliotis, C. Xenophontos and G. Georgiou, Analysis of the singular function boundary integral method for two-dimensional biharmonic problems with a boundary singularity, Proc. of the 2nd South-East European Conference on Computational Mechanics, M. Papadrakakis, M. Kojic, V. Papadopoulos (Eds), Rhodes, Greece, 22 - 24 June (2009).
E. Christodoulou, C. Xenophontos and G. Georgiou, The singular function boundary integral method for elliptic problems with boundary singularities, Proc. of the 6th GRACM International Congress on Computational Mechanics, Thessaloniki, Greece, 19 - 21 June (2008).
L. Oberbroeckling and C. Xenophontos An hp finite element method for singularly perturbed systems of reaction diffusion equations, Proc. Appl. Math. Mech. 7, pp. 2020055 - 2020056 (2007). (PDF file.)
C. Xenophontos, G. Georgiou and M. Elliotis, A Singular Function Boundary Integral Method for Elliptic Problems with Singularities, Proc. Appl. Math. Mech. 7, pp. 2020129 - 2020130 (2007). (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, Solution of the stick-slip problem with the singular function boundary integral method, Proceedings of the 5th GRACM Congress on Computational Mechanics, 29 June - 1 July, 2005, Limassol, Cyprus. (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, The singular function boundary integral method for a two-dimensional fracture problem, Proceedings of the 5th GRACM Congress on Computational Mechanics, 29 June - 1 July, 2005, Limassol, Cyprus. (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, Numerical Solutions of Laplacian Problems over L-shaped Domains and Calculations of the Generalized Stress Intensity Factors, Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), H. A. Mang, F. G. Rammerstorfer and J. Eberhardsteiner (Eds), ISBN: 3-9501554-0-6, July 7 - 12, 2002, Vienna, Austria. (PDF file.)
C. Xenophontos, J. Kurtz and S. R. Fulton, On the uniform approximation of the Reissner-Mindlin plate model by p/hp finite element methods, Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), July 7 - 12, 2002, Vienna, Austria, H. A. Mang, F. G. Rammerstorfer and J. Eberhardsteiner (Eds), ISBN: 3-9501554-0-6. (PDF file.)
C. Xenophontos, J. Kurtz and S. R. Fulton, On the approximation of the Reissner-Mindlin plate model by the p/hp version of the finite element method, Proceedings of the 4th GRACM Congress on Computational Mechanics, 27 - 29 June, 2002, Patra, Greece. (PDF file.)
M. Elliotis, G. Georgiou and C. Xenophontos, Numerical calculation of the leading singular coefficients in Laplacian problems over L-shaped domains, Proceedings of the 4th GRACM Congress on Computational Mechanics, 27 - 29 June, 2002, Patra, Greece. (PDF file.)
M. Suri and C. Xenophontos, Reliability of an hp algorithm for buckling analysis , Proceedings of IASS-IACM 2000: Fourth International Colloq. on Computation of Shell and Spatial Structures, Chania, Greece, June 5-7, 2000. (PDF file.)
B. Jeremic, C. Xenophontos and S. Sture, Modeling of continuous localization of deformation, R. Ghanem and N. Jones Editors, Proceedings of 13th ASCE Conference, Baltimore, MD, June 1999. (PDF file.)
C. Xenophontos, Boundary layer resolution via the hp finite element method - Symposium on Rheology and Computational Fluid Mechanics, Proceedings , G. Georgiou (Ed), pp. 113 - 120 (1996).

Technical Reports
M. J. Melenk, C. Xenophontos and L. Oberbroeckling, Robust exponential convergence of hp-FEM for singularly perturbed systems of reaction-diffusion systems with multiple scales, ASC Report No. 31-2011, Institute for Analysis and Scientific Computing, Vienna Institute of Technology. (PDF file.)
M. J. Melenk, C. Xenophontos and L. Oberbroeckling, Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs, SC Report No. 29-2011, Institute for Analysis and Scientific Computing, Vienna Institute of Technology. (PDF file.)
M. Knapp and C. Xenophontos, Numerical analysis meets number theory: using rootfinding methods to calculate inverses mod p n, Technical Report 2004-02, Mathematical Sciences Department, Loyola College, 2004. (PDF file , PS file.)
J. Kurtz, C. Xenophontos and S. Fulton, An hp MITC finite element method for Reissner-Mindlin plates with smooth boundaries, Technical Report 2003-01, Dept. of Math. & Comp. Sci., Clarkson University, 2003. (PDF file , PS file.)
C. Xenophontos and S. R. Fulton, MAPLE Turorial 4: Matrices and Vectors, Technical Report 99-06, Dept. of Math. & Comp. Sci., Clarkson University, 1999. (PDF file.)
S. R. Fulton and C. Xenophontos, MAPLE Turorial 3: Derivatives and Integrals, Technical Report 99-05, Dept. of Math. & Comp. Sci., Clarkson University, 1999. (PDF file.)
S. R. Fulton and C. Xenophontos, MAPLE Turorial 2: Functions, Plots and Equations, Technical Report 99-04, Dept. of Math. & Comp. Sci., Clarkson University, 1999. (PDF file.)
S. R. Fulton and C. Xenophontos, MAPLE Turorial 1: Getting Started, Technical Report 99-03, Dept. of Math. & Comp. Sci., Clarkson University, 1999. (PDF file.)
C. Xenophontos, A Beginner's Guide to MATLAB, Technical Report 98-02, Dept. of Math. & Comp. Sci., Clarkson University, 1998. (PDF file.)

Other
G. Georgiou and C. Xenophontos, Introduction to MATLAB (in Greek), Kantzilaris Publications, Nicosia, 2007 (ISBN: 978-9963-644-57-52007). (PDF file.)
C. Xenophontos, A beginner's guide to MATLAB (in Greek). (PDF file.)
C. Xenophontos, A formula for the nth derivative of the quotient of two functions, 2007. (PDF file.)
C. Xenophontos, The hp finite element method for singularly perturbed problems, Ph.D. Dissertation, University of Maryland, 1996. (PDF file.)

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