TY - JOUR
T1 - Symplectic Hamiltonian finite element methods for linear elastodynamics
AU - Sánchez, Manuel A.
AU - Cockburn, Bernardo
AU - Nguyen, Ngoc Cuong
AU - Peraire, Jaime
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/8/1
Y1 - 2021/8/1
N2 - We present a class of high-order finite element methods that can conserve the linear and angular momenta as well as the energy for the equations of linear elastodynamics. These methods are devised by exploiting and preserving the Hamiltonian structure of the equations of linear elastodynamics. We show that several mixed finite element, discontinuous Galerkin, and hybridizable discontinuous Galerkin (HDG) methods belong to this class. We discretize the semidiscrete Hamiltonian system in time by using a symplectic integrator in order to ensure the symplectic properties of the resulting methods, which are called symplectic Hamiltonian finite element methods. For a particular semidiscrete HDG method, we obtain optimal error estimates and present, for the symplectic Hamiltonian HDG method, numerical experiments that confirm its optimal orders of convergence for all variables as well as its conservation properties.
AB - We present a class of high-order finite element methods that can conserve the linear and angular momenta as well as the energy for the equations of linear elastodynamics. These methods are devised by exploiting and preserving the Hamiltonian structure of the equations of linear elastodynamics. We show that several mixed finite element, discontinuous Galerkin, and hybridizable discontinuous Galerkin (HDG) methods belong to this class. We discretize the semidiscrete Hamiltonian system in time by using a symplectic integrator in order to ensure the symplectic properties of the resulting methods, which are called symplectic Hamiltonian finite element methods. For a particular semidiscrete HDG method, we obtain optimal error estimates and present, for the symplectic Hamiltonian HDG method, numerical experiments that confirm its optimal orders of convergence for all variables as well as its conservation properties.
KW - Discontinuous Galerkin methods
KW - Elastodynamics
KW - Hybridizable discontinuous Galerkin methods
KW - Mixed methods
KW - Symplectic Hamiltonian finite element methods
UR - http://www.scopus.com/inward/record.url?scp=85105547749&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85105547749&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.113843
DO - 10.1016/j.cma.2021.113843
M3 - Article
AN - SCOPUS:85105547749
SN - 0045-7825
VL - 381
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113843
ER -