### preprints

Finite Element Analysis of Cauchy-Born Approximations to Atomistic Models

(with E. Süli) Preprint
pdf

Interior a posteriori error estimates for
time discrete approximations of parabolic problems

(with C. Lubich) Preprint
pdf

Helmholtz equation with artificial boundary
conditions in a two-dimensional wavequide

(with D. Mitsoudis, M. Plexoussakis) Preprint
pdf

The eﬀect of mesh modiﬁcation in time on the error control of fully discrete
approximations for parabolic equations

(with E. Bänsch and F. Karakatsani)
pdf

A posteriori error control for fully discrete Crank-Nicolson schemes

(with E. Bänsch and F. Karakatsani)
pdf

Stress-based atomistic/continuum coupling: a new variant of the quasicontinuum approximation

(with C. Ortner and E. Süli) Preprint
pdf

A posteriori L∞(L2 )-error bounds in ﬁnite element approximation of the wave equation

(with E.
Georgoulis and O. Lakkis) Preprint pdf

A new discontinuous Galerkin scheme for the numerical solution of ﬂow problems with discon-
tinuities

(with I. Toulopoulos) Int. J. Numer. Meth. Fluids To appear.
pdf

### inverse chronological listing

A Priori Error Analysis of Two Force-Based
Atomistic/Continuum Hybrid Models of a Periodic
Chain

(with C. Ortner and E. Süli) Numer. Math. 119 (2011) 83 - 121
pdf

Galerkin and Runge-Kutta methods: Unified formulation, a posteriori error estimates and nodal superconvergence

(with G. Akrivis and R. Nochetto) Numer. Math. 118 (2011), 429 - 456
pdf

Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations

(with I. Kyza) SIAM J. Numer. Anal. 49 (2011) 405 - 426
pdf

Error control for time-splitting spectral approximations of the semiclassical Schr¨odinger equation

(with I. Kyza, M. Plexoussakis) IMA J. Numer. Anal. 31 (2011), 416–441
pdf

Entropy conservative schemes and adaptive mesh selection for hyperbolic conservation laws

(with
Ch. Arvanitis and N. Sfakianakis) J. Hyp. Diff. Eq. 7 (2010), 383–404.
pdf

Sharply localized pointwise a posteriori error estimates for parabolic problems

(with
A. Demlow) Math. Comp. 79 (2010), 1233-1262. pdf

Pointwise a posteriori error estimates for parabolic problems via el liptic reconstruction

(with
A. Demlow, O. Lakkis) SIAM J. Numer. Anal. 47 (2009), 2157-2176
pdf

A posteriori error control for Runge-Kutta discretizations of evolution problems

(with G. Akrivis
and R. Nochetto), Numer. Math. 114 (2009), 133 - 160
pdf

A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic
problems in Banach spaces

(with E. Cuesta), Numer. Math. 110, (2008), 257-275
pdf

A posteriori estimates for approximations of time dependent Stokes equations

(with F. Karakatsani) IMA Journal of Numerical Analysis 27 (2007) 741-764
pdf

Error control of generalized DG methods for
hyperbolic conservation laws

(with A. Dedner and M. Ohlberger) SIAM J. Numer. Anal. 45 (2007), 514–538
pdf

Space and Time Reconstructions in A Posteriori Analysis of Evolution Problems, ESAIM: Proceedings, September 2007, vol. 21, 31–44 pdf

Elliptic reconstruction and a posteriori error analysis for fully discrete linear parabolic problems

(with O. Lakkis) Math. Comp. 75 (2006), 1627–1658
pdf

A posteriori error analysis for higher order dissipative methods for evolution
problems

(with R. Nochetto) Numer. Math. 104 (2006), 489–514.
pdf

A posteriori error estimates for the Crank-Nicolson method for parabolic equations

(with G. Akrivis and R. Nochetto) Math. Comp. 75 (2006), 511-531.
pdf

Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations

(with O. Karakashian) Math.Comp. 74 (2005), 85-102 pdf-file

Stability and convergence of relaxation finite element schemes for the incompressible Navier-Stokes equations (with Th. Katsaounis and C. Simeoni) Proceedings of the Conference on Hy- perbolic Problems, Yakohama Pupl., 2005, 87–92 pdf-file

Galerkin time stepping schemes for nonlinear parabolic Problems

(with G. Akrivis) Math. Model. Numer. Anal. 38 (2004) 261-289
pdf-file

Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws

(with Ch. Arvanitis and A. Tzavaras) SIAM J. Numer. Anal. 42 (2004), 1357-1393
pdf-file

Relaxation models and finite element schemes for the shallow water equations

(with Th. Katsaounis) Hyperbolic problems: theory, numerics, applications, 621-631, Springer, Berlin, 2003
pdf-file

An extended version (report ENS)
pdf-file

Sharp CFL, discrete kinetic formulation and entropic schemes for scalar conservation laws

(with B. Perthame) SIAM J. Numer. Anal. 41 (2003), no. 3, 1032-1051
paper -
pdf-file

Elliptic reconstruction and a posteriori error estimates for parabolic problems

(with R. Nochetto) SIAM J. Numer. Anal. 41 (2003), no. 4, 1585-1594
paper -
pdf-file

A posteriori error estimates for a finite volume method for Stokes equations

(with P. Chatzipandelidis and M. Plexousakis) Appl. Numer. Math. 46 (2003), no. 1, 45-58.
pdf-file

Optimal rate of convergence for anisotropic vanishing viscosity limit of a scalar balance law

(with B. Perthame) SIAM J. Math. Anal. 34 (2003), no. 6, 1300-1307
paper -
pdf-file

Finite volume relaxation schemes for multidimensional conservation laws

(with Th. Katsaounis) Mathematics of Computation 70 (2001), 533-553.
paper -
ps-file -
Technical Report including Fully Discrete Schemes

Adaptive finite element relaxation schemes for hyperbolic systems of conservation laws

(with Ch. Arvanitis and Th. Katsaounis) Math. Model. Anal. Numer. 35 (2001), no. 1, 17-33.
pdf-file

Convergence of the discontinuous Galerkin method for nonlinear parabolic problems

(with G. Akrivis) preprint

Two a posteriori error estimates for one dimensional scalar conservation laws

(with L. Gosse) SIAM J. Numer. Anal. 38 (2000) 964-988. paper - ps-file

Finite volume schemes for Hamilton Jacobi equations

(with G. Kossioris and P. Souganidis) Numer. Math. 83 (1999), 427 - 442 pdf-file

Convergence and error estimates for relaxation schemes for multidimensional conservation laws

(with M. Katsoulakis and G. Kossioris) Comm. Part. Dif. Equations 24 (1999) 395 - 424 ps- file

Implicit-explicit multistep finite element methods for nonlinear parabolic problems

(with G. Akrivis and M. Crouzeix)

Mathematics of Computation, 67 (1998), 457-477 pdf file

A space time finite element method for the nonlinear Schroedinger equation: the discontinuous Galerkin method

(with O. Karakashian) Mathematics of Computation 67 (1998), 479-499 ps file

Implicit-explicit multistep methods for quasilinear parabolic equations

(with G. Akrivis and M. Crouzeix) Numer. Math. 82 (1999) 521 - 541. pdf-file

A space time finite element method for the nonlinear Schroedinger equation. II: the continuous Galerkin method

(with O. Karakashian) SIAM J. Numer. Anal. 36 (1999) 1779 -1807 ps-file

A posteriori error estimates for numerical approximations to scalar conservation

laws: schemes satisfying strong and weak entropy inequalities

(with L. Gosse) IACM-FORTH Technical report 98.4 (1998). ps-file

On the stability of the discontinuous Galerkin method for the heat equation

(with I. Babuska) SIAM J. Numer. Anal. 34 (1997) 389-401 ps file

Analysis and finite element methods for a fluid-solid interaction problem in one dimension

(with I. Babuska and F. Ihlenburg)

Math. Models Meth. Appl. Sc. 6 (1996) 1119-1141
pdf

High-order fully discrete methods for the equations of elastic wave propagation with absorbing boundary conditions, IMA J. Numer. Anal. 15 (1995) 377-404

Error estimates of Galerkin FEM for a coupled set of Helmholtz equations in one dimension

(with F. Ihlenburg) (Proceedings of 11 th GAMM), Kiel (1995)

Time-discrete finite element schemes for Maxwell's equations (with P. Monk) RAIRO Math. Model. Anal. Numer. 29 (1995) 171-197

Finite element approximations of nonlinear elastic waves, Mathematics of Computation 61 (1993) 569-594 pdf

On mixed finite element methods for linear elastodynamics, Numer. Math. 61 (1992) 235-260 pdf

Cosine methods for a class of semilinear second-order wave equations, Comput. Math. Applic. 19 (1990) 19-34