Geodesic
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

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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.

DOI : 10.1051/m2an/2018037
Classification : 65M60, 65N30
Keywords: Hybridizable discontinuous Galerkin method, fifth-order, Korteweg-de Vries equation, DG

Chen, Yanlai 1 ; Dong, Bo 1 ; Jiang, Jiahua 1

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},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {6},
     year = {2018},
     doi = {10.1051/m2an/2018037},
     zbl = {1417.65168},
     mrnumber = {3905190},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018037/}
}
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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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