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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. | 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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| + | == Abstract == | ||
| + | <pdf>Media:Draft_Sanchez Pinedo_357740873508_abstract.pdf</pdf> | ||
| + | |||
| + | == Full Paper == | ||
| + | <pdf>Media:Draft_Sanchez Pinedo_357740873508_paper.pdf</pdf> | ||
Latest revision as of 16:06, 25 November 2022
Summary
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.
Abstract
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Published on 24/11/22
Accepted on 24/11/22
Submitted on 24/11/22
Volume Computational Applied Mathematics, 2022
DOI: 10.23967/eccomas.2022.206
Licence: CC BY-NC-SA license
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