Abstract:
In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is
discretized in space using stabilized finite elements. On the one hand, stability and convergence analyses of
the fully discrete numerical schemes are presented using different time integration schemes and appropriate
functional settings. On the other hand, we use Fourier techniques (also known as von Neumann analysis) in
order to analyze stability, dispersion and dissipation. Numerical convergence tests are presented for various
time integration schemes, polynomial interpolations (for the spatial discretization), stabilization methods,
and variational forms. To analyze the behavior of the different schemes considered, a 1D wave propagation
problem is solved.
Description:
In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is
discretized in space using stabilized finite elements. On the one hand, stability and convergence analyses of
the fully discrete numerical schemes are presented using different time integration schemes and appropriate
functional settings. On the other hand, we use Fourier techniques (also known as von Neumann analysis) in
order to analyze stability, dispersion and dissipation. Numerical convergence tests are presented for various
time integration schemes, polynomial interpolations (for the spatial discretization), stabilization methods,
and variational forms. To analyze the behavior of the different schemes considered, a 1D wave propagation
problem is solved.
