Workshop on Numerical Methods and Analysis in CFD - Abstract
Stocker, Paul
The Galbrun's equation with additional rotational and gravitational terms model stellar oscillations. Recently, well-posedness of the continuous problem was proven, by using a suitable generalized Helmholtz decomposition in the analysis. In the discretization we aim to preserve a discrete version of the generalized Helmholtz decomposition, which is crucial for stability and helpful for the numerical analysis. The decomposition presents a strong connection between stable discretizations for the Galbrun equations and Stokes and nearly incompressible linear elasticity problems. We derive conditions on the discretization that preserve the structural properties of the continuous problem and introduce the tools needed for the numerical analysis.