Robust finite element discretizations for a simplified Galbrun's equation

arXiv (Cornell University)

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.

Authors 3

1. Tilman Aleman Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik (IGPM) , RWTH Aachen University Templergraben 55 , 52062 Aachen , Germany

2. Christoph Lehrenfeld

   University of Göttingen

   Affiliation as printed

   Institute for Numerical and Applied Mathematics , University of Göttingen Lotzestr. 16-18 , 37083 Göttingen , Germany

3. Paul Stocker

   University of Göttingen

   Affiliation as printed

   Institute for Numerical and Applied Mathematics , University of Göttingen Lotzestr. 16-18 , 37083 Göttingen , Germany