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A high‐order implicit hybridizable discontinuous Galerkin method for the Benjamin‐Bona‐Mahony equation
Author(s) -
Fabien Maurice S.
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4896
Subject(s) - discontinuous galerkin method , scheme (mathematics) , mathematics , time stepping , space (punctuation) , order (exchange) , conservation law , mathematical analysis , finite element method , computer science , physics , discretization , finance , economics , thermodynamics , operating system
Summary This article introduces an efficient numerical scheme for the solution of the Benjamin‐Bona‐Mahony equation. The scheme is fully implicit, and combines high‐order time stepping and a hybridizable discontinuous Galerkin method in space. Implicit time stepping allows for larger time steps, while remaining robust for long‐time simulations. It is shown that the scheme is energy stable, and conserves mass. Computational experiments demonstrate that the scheme is high‐order accurate, robust, and possesses good conservation properties.