Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws

Christos Arvanitis; Theodoros Katsaounis; Charalambos Makridakis

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 1, page 17-33
  • ISSN: 0764-583X

Abstract

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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 scalar problems and the system of elastodynamics.

How to cite

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Arvanitis, Christos, Katsaounis, Theodoros, and Makridakis, Charalambos. "Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws." ESAIM: Mathematical Modelling and Numerical Analysis 35.1 (2010): 17-33. <http://eudml.org/doc/197500>.

@article{Arvanitis2010,
abstract = { 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 scalar problems and the system of elastodynamics. },
author = {Arvanitis, Christos, Katsaounis, Theodoros, Makridakis, Charalambos},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Conservation laws; finite elements; adaptive methods.; conservation laws; adaptive methods; semidiscretization; consistency; adaptive refinement; shock; mesh coarsening; Runge-Kutta methods; Burgers equation; nonlinear elastodynamics},
language = {eng},
month = {3},
number = {1},
pages = {17-33},
publisher = {EDP Sciences},
title = {Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws},
url = {http://eudml.org/doc/197500},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Arvanitis, Christos
AU - Katsaounis, Theodoros
AU - Makridakis, Charalambos
TI - Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 17
EP - 33
AB - 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 scalar problems and the system of elastodynamics.
LA - eng
KW - Conservation laws; finite elements; adaptive methods.; conservation laws; adaptive methods; semidiscretization; consistency; adaptive refinement; shock; mesh coarsening; Runge-Kutta methods; Burgers equation; nonlinear elastodynamics
UR - http://eudml.org/doc/197500
ER -

References

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