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a review article for reconstruction methods

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Papers by class of problems

Conservation Laws <

Entropy conservative schemes and adaptive mesh selection for hyperbolic conservation laws
(with Ch. Arvanitis and N. Sfakianakis) Preprint pdf

A new discontinuous Galerkin scheme for the numerical solution of flow problems with discon- tinuities
(with I. Toulopoulos) Preprint 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

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

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

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

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

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

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

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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 >

time discrete schemes

space and fully discrete schemes

nonlinear problems

Geometrical driven adaptivity >

all papers >

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