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Title: 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.
 [1] ;  [2]
  1. Delft Univ. of Technology, Delft (The Netherlands)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0898-1221; PII: S0898122116300293
Grant/Contract Number:
AC04-94AL85000; 14-017511
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 71; Journal Issue: 11; Journal ID: ISSN 0898-1221
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; least-squares; mimetic methods; spectral element method; mass conservation
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1351654