A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition
Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximated by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- 14-017511; AC04-94AL85000
- OSTI ID:
- 1631365
- Alternate ID(s):
- OSTI ID: 1259851; OSTI ID: 1351654
- Report Number(s):
- SAND-2015-7054J; S0898122116300293; PII: S0898122116300293
- Journal Information:
- Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 71 Journal Issue: 11; ISSN 0898-1221
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
Web of Science
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