Robust finite element discretizations for a simplified Galbrun's equation
Numerical Analysis
2022-06-01 v1 Numerical Analysis
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.
Cite
@article{arxiv.2205.15650,
title = {Robust finite element discretizations for a simplified Galbrun's equation},
author = {Tilman Alemán and Martin Halla and Christoph Lehrenfeld and Paul Stocker},
journal= {arXiv preprint arXiv:2205.15650},
year = {2022}
}
Comments
12 pages, 3 figures