TY - JOUR
T1 - Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations
AU - Zhang , Qian
AU - Xu , Yan
AU - Shu , Chi-Wang
JO - Communications in Computational Physics
VL - 2
SP - 321
EP - 356
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0027
UR - https://global-sci.org/intro/article_detail/cicp/19117.html
KW - Discontinuous Galerkin method, Fornberg-Whitham type equation, dissipative
scheme, conservative scheme, error estimates.
AB - <p style="text-align: justify;">In this paper, we construct high order energy dissipative and conservative
local discontinuous Galerkin methods for the Fornberg-Whitham type equations. We
give the proofs for the dissipation and conservation for related conservative quantities. The corresponding error estimates are proved for the proposed schemes. The
capability of our schemes for different types of solutions is shown via several numerical experiments. The dissipative schemes have good behavior for shock solutions,
while for a long time approximation, the conservative schemes can reduce the shape
error and the decay of amplitude significantly.</p>