# 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

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topArvanitis, 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 -

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