We develop and analyze the first hybridizable discontinuous Galerkin (HDG) method for solving fifth-order Korteweg-de Vries (KdV) type equations. We show that the semi-discrete scheme is stable with proper choices of the stabilization functions in the numerical traces. For the linearized fifth-order equations, we prove that the approximations to the exact solution and its four spatial derivatives as well as its time derivative all have optimal convergence rates. The numerical experiments, demonstrating optimal convergence rates for both the linear and nonlinear equations, validate our theoretical findings.
Keywords: Hybridizable discontinuous Galerkin method, fifth-order, Korteweg-de Vries equation, DG
Chen, Yanlai 1 ; Dong, Bo 1 ; Jiang, Jiahua 1
@article{M2AN_2018__52_6_2283_0,
author = {Chen, Yanlai and Dong, Bo and Jiang, Jiahua},
title = {Optimally convergent hybridizable discontinuous {Galerkin} method for fifth-order {Korteweg-de} {Vries} type equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2283--2306},
year = {2018},
publisher = {EDP Sciences},
volume = {52},
number = {6},
doi = {10.1051/m2an/2018037},
zbl = {1417.65168},
mrnumber = {3905190},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2018037/}
}
TY - JOUR AU - Chen, Yanlai AU - Dong, Bo AU - Jiang, Jiahua TI - Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 2283 EP - 2306 VL - 52 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2018037/ DO - 10.1051/m2an/2018037 LA - en ID - M2AN_2018__52_6_2283_0 ER -
%0 Journal Article %A Chen, Yanlai %A Dong, Bo %A Jiang, Jiahua %T Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 2283-2306 %V 52 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2018037/ %R 10.1051/m2an/2018037 %G en %F M2AN_2018__52_6_2283_0
Chen, Yanlai; Dong, Bo; Jiang, Jiahua. Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2283-2306. doi: 10.1051/m2an/2018037
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