Displaying similar documents to “Adaptive finite element relaxation schemes for hyperbolic conservation laws”

Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws

Christos Arvanitis, Theodoros Katsaounis, Charalambos Makridakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering ...

Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids

Bruno Després, Frédéric Lagoutière (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.