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math.NA2026
High-order Conservative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg-de Vries Equation and the Hirota-Satsuma KdV System
M. Shan Tariq, Yanlai Chen, Bo Dong
We develop new conservative discontinuous Galerkin (DG) methods for nonlinear wave problems, focusing on the generalized Korteweg-de Vries (gKdV) equation and the coupled Hirota-Sa…
math.NA2022
Numerical investigations on the resonance errors of multiscale discontinuous Galerkin methods for one-dimensional stationary Schrödinger equation
Bo Dong, Wei Wang
In this paper, numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high order multiscale discon…
math.NA2017
Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations
Bo Dong, Jiahua Jiang, Yanlai Chen
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 sch…