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Stabilized finite elements for time‐harmonic waves in incompressible and nearly incompressible elastic solids
Author(s) -
Barbone Paul E.,
Nazari Navid,
Harari Isaac
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6169
Subject(s) - compressibility , discretization , finite element method , curl (programming language) , galerkin method , mathematics , mathematical analysis , pressure correction method , mechanics , physics , classical mechanics , computer science , thermodynamics , programming language
Summary The propagation of waves in elastic solids at or near the incompressible limit is of interest in many current and emerging applications. Standard low‐order Galerkin finite element discretization struggles with both incompressibility and wave dispersion. Galerkin least squares stabilization is known to improve computational performance of each of these ingredients separately. A novel approach of combined pressure‐curl stabilization is presented, facilitating the use of continuous, equal‐order interpolation of displacements and pressure. The pressure stabilization parameter is determined by stability considerations, while the curl stabilization parameter is determined by dispersion considerations. The proposed pressure‐curl–stabilized scheme provides stable and accurate results on a variety of numerical tests for incompressible and nearly incompressible elastic waves computed with linear elements.