Symplectic-mixed finite element approximation of linear acoustic wave equations
The authors develop a finite element method for the linear acoustic wave equation \[ \rho p_{t} + \nabla u = f, \] \[ \kappa ^{-1}u_{t} + \nabla p = g, \] on the polyhedral domain by space variables \(\Omega \subset \mathbb R^{d}\) and finite time interval \([0,T]\) with the usual initial conditions and the boundary condition \( u \nu = 0\) on \(\partial \Omega\), where \( \nu \) is the unit outward normal to \( \Omega\). The obtained approximate scheme preserves the essential properties of the initial problem, especially the positive definite functional of energy. The stability of the method is proved imposing several conditions on the time and space steps and other parameters of the problem.
scientific article; zbMATH DE number 6502658
scientific article