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arXiv · 2205.15650

Robust finite element discretizations for a simplified Galbrun's equation

Tilman Alemán·Martin Halla·Christoph Lehrenfeld·Paul Stocker
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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.

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Tilman Alemán, Martin Halla, Christoph Lehrenfeld, Paul Stocker. 2022-05-31. Robust finite element discretizations for a simplified Galbrun's equation. https://arxiv.org/abs/2205.15650

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