In this paper we present an a priori error estimate of the Runge–Kutta discontinuous Galerkin method for solving symmetrizable conservation laws, where the time is discretized with the third order explicit total variation diminishing Runge–Kutta method and the finite element space is made up of piecewise polynomials of degree . Quasi-optimal error estimate is obtained by energy techniques, for the so-called generalized E-fluxes under the standard temporal-spatial CFL condition , where is the element length and is time step, and is a positive constant independent of and . Optimal estimates are also considered when the upwind numerical flux is used.
DOI : 10.1051/m2an/2014063
Mots-clés : Discontinuous Galerkin method, Runge–Kutta method, error estimates, symmetrizable system of conservation laws, energy analysis
@article{M2AN_2015__49_4_991_0, author = {Luo, Juan and Shu, Chi-Wang and Zhang, Qiang}, title = {A priori error estimates to smooth solutions of the third order {Runge{\textendash}Kutta} discontinuous {Galerkin} method for symmetrizable systems of conservation laws}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {991--1018}, publisher = {EDP-Sciences}, volume = {49}, number = {4}, year = {2015}, doi = {10.1051/m2an/2014063}, mrnumber = {3371901}, zbl = {1327.65193}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2014063/} }
TY - JOUR AU - Luo, Juan AU - Shu, Chi-Wang AU - Zhang, Qiang TI - A priori error estimates to smooth solutions of the third order Runge–Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 991 EP - 1018 VL - 49 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2014063/ DO - 10.1051/m2an/2014063 LA - en ID - M2AN_2015__49_4_991_0 ER -
%0 Journal Article %A Luo, Juan %A Shu, Chi-Wang %A Zhang, Qiang %T A priori error estimates to smooth solutions of the third order Runge–Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 991-1018 %V 49 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2014063/ %R 10.1051/m2an/2014063 %G en %F M2AN_2015__49_4_991_0
Luo, Juan; Shu, Chi-Wang; Zhang, Qiang. A priori error estimates to smooth solutions of the third order Runge–Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 991-1018. doi : 10.1051/m2an/2014063. http://archive.numdam.org/articles/10.1051/m2an/2014063/
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