643	RWTH Publication No: 981183        2022
TITLE	Robust finite element discretizations for a simplified Galbrun's equation
AUTHORS	Tilman Alemán, Martin Halla, Christoph Lehrenfeld, Paul Stocker
ABSTRACT	Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for different finite element schemes on a simplified version of the equations. The considered PDE is a second order indefinite vector-PDE which remains if only the highest order terms of Galbrun's equation are taken into account. A key property for stability is a Helmholtz-type decomposition which results in a strong connection between stable discretizations for Galbrun's equation and Stokes and nearly incompressible linear elasticity problems.
KEYWORDS	Galbrun’s equation, FEM, discontinuous Galerkin, Helmholtz decomposition