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The main purpose of this paper is to give stability analysis and error estimates of the local discontinuous Galerkin (LDG) methods coupled with three specific implicit-explicit (IMEX) Runge–Kutta time discretization methods up to third order accuracy, for solving one-dimensional time-dependent linear fourth order partial differential equations. In the time discretization, all the lower order derivative terms are treated explicitly and the fourth order derivative term is treated implicitly. By the aid of energy analysis, we show that the IMEX-LDG schemes are unconditionally energy stable, in the sense that the time step is only required to be upper-bounded by a constant which is independent of the mesh size . The optimal error estimate is also derived by the aid of the elliptic projection and the adjoint argument. Numerical experiments are given to verify that the corresponding IMEX-LDG schemes can achieve optimal error accuracy.
Wang, Haijin 1 ; Zhang, Qiang 2 ; Shu, Chi-Wang 3
@article{M2AN_2017__51_5_1931_0,
author = {Wang, Haijin and Zhang, Qiang and Shu, Chi-Wang},
title = {Stability analysis and error estimates of local discontinuous {Galerkin} methods with implicit-explicit time-marching for the time-dependent fourth order {PDEs}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1931--1955},
publisher = {EDP-Sciences},
volume = {51},
number = {5},
year = {2017},
doi = {10.1051/m2an/2017017},
zbl = {1407.65204},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017017/}
}
TY - JOUR AU - Wang, Haijin AU - Zhang, Qiang AU - Shu, Chi-Wang TI - Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1931 EP - 1955 VL - 51 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017017/ DO - 10.1051/m2an/2017017 LA - en ID - M2AN_2017__51_5_1931_0 ER -
%0 Journal Article %A Wang, Haijin %A Zhang, Qiang %A Shu, Chi-Wang %T Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1931-1955 %V 51 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017017/ %R 10.1051/m2an/2017017 %G en %F M2AN_2017__51_5_1931_0
Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang. Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1931-1955. doi: 10.1051/m2an/2017017
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