recent preprints
a review article for reconstruction methods
.
Papers by class of problems
Conservation Laws >
finite element relaxation schemes
finite difference and kinetic schemes
finite volumes
a posteriori estimates
geometrical driven adaptivity
Wave Equations >
finite elements for linear elastodynamics
nonlinear wave equations
Parabolic Problems >
analysis of the time dg-method
implicit-explicit schemes for nonlinear problems
a posteriori estimates for linear problems
conditional error control for nonlinear problems
Other Problems >
standard schemes for the Helmholtz equation
Schroedinger equations
finite volumes for Hamilton-Jacobi
Stokes and Navier-Stokes
.
.
Papers by computational methods (and methodologies)
Time and space-time finite elements >
a priori analysis of the time dg-method
a posteriori estimates
A posteriori error control / reconstruction methods <
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
A posteriori L∞(L2 )-error bounds in finite element approximation of the wave equation
(with E.
Georgoulis and O. Lakkis) Preprint 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
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
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
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
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