SPEAKER: Manuel A. Sánchez Uribe (Instituto de Ingeniería Matemática y Computacional (IMC))
Location: Only online through TEAMS
TITLE: Symplectic Hamiltonian HDG methods for wave propagation
ABSTRACT:
In this talk, we introduce 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 scalar wave and elastodynamics.
These methods are devised by exploiting and preserving the Hamiltonian structure of the equations. 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 to ensure the symplectic properties of the resulting methods, which are called symplectic Hamiltonian finite element methods. For semidiscrete HDG methods,
we obtain optimal error estimates and present numerical experiments that confirm its optimal orders of convergence for all variables as well as its conservation properties.
