A spectral mimetic least-squares method

Bochev, Pavel; Gerritsma, Marc

doi:10.1016/j.camwa.2014.09.014

A spectral mimetic least-squares method

Journal Article · Mon Dec 01 00:00:00 EST 2014 · Computers and Mathematics with Applications (Oxford)

DOI:https://doi.org/10.1016/j.camwa.2014.09.014· OSTI ID:1484076

Bochev, Pavel; Gerritsma, Marc

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1484076

Alternate ID(s):: OSTI ID: 1140934

Report Number(s):: SAND--2014-1827J; S0898122114004623; PII: S0898122114004623

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Journal Issue: 11 Vol. 68; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (16)

A locally conservative least-squares method for Darcy flows Bochev, P. B.; Gunzburger, M. D. Communications in Numerical Methods in Engineering, Vol. 24, Issue 2 https://doi.org/10.1002/cnm.957	journal	December 2006
Discrete Hodge operators Hiptmair, R. Numerische Mathematik, Vol. 90, Issue 2 https://doi.org/10.1007/s002110100295	journal	December 2001
Mass- and Momentum Conservation of the Least-Squares Spectral Element Method for the Stokes Problem Proot, Michael M. J.; Gerritsma, Marc I. Journal of Scientific Computing, Vol. 27, Issue 1-3 https://doi.org/10.1007/s10915-005-9030-3	journal	December 2005
Local error estimation and adaptive remeshing scheme for least-squares mixed finite elements Carey, G. F.; Pehlivanov, A. I. Computer Methods in Applied Mechanics and Engineering, Vol. 150, Issue 1-4 https://doi.org/10.1016/S0045-7825(97)00098-4	journal	December 1997
Least-squares for second-order elliptic problems Bramble, James H.; Lazarov, Raytcho D.; Pasciak, Joseph E. Computer Methods in Applied Mechanics and Engineering, Vol. 152, Issue 1-2 https://doi.org/10.1016/S0045-7825(97)00189-8	journal	January 1998
The convergence of mimetic discretization for rough grids Hyman, J. M.; Steinberg, S. Computers & Mathematics with Applications, Vol. 47, Issue 10-11 https://doi.org/10.1016/j.camwa.2004.06.008	journal	May 2004
An alternative least-squares formulation of the Navier–Stokes equations with improved mass conservation Heys, J. J.; Lee, E.; Manteuffel, T. A. Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.05.005	journal	September 2007
Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution Kreeft, Jasper; Gerritsma, Marc Journal of Computational Physics, Vol. 240 https://doi.org/10.1016/j.jcp.2012.10.043	journal	May 2013
Mimetic finite difference method Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.07.031	journal	January 2014
Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms Palha, Artur; Rebelo, Pedro Pinto; Hiemstra, René Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.08.005	journal	January 2014
Finite element exterior calculus, homological techniques, and applications Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar Acta Numerica, Vol. 15 https://doi.org/10.1017/S0962492906210018	journal	May 2006
Geometrical localisation of the degrees of freedom for Whitney elements of higher order Bossavit, A.; Rapetti, F. IET Science, Measurement & Technology, Vol. 1, Issue 1 https://doi.org/10.1049/iet-smt:20060022	journal	January 2007
On Mass‐Conserving Least‐Squares Methods Heys, J. J.; Lee, E.; Manteuffel, T. A. SIAM Journal on Scientific Computing, Vol. 28, Issue 5 https://doi.org/10.1137/050640928	journal	January 2006
On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles Bochev, Pavel; Gunzburger, Max SIAM Journal on Numerical Analysis, Vol. 43, Issue 1 https://doi.org/10.1137/S003614290443353X	journal	January 2005
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation Chang, C. L.; Nelson, John J. SIAM Journal on Numerical Analysis, Vol. 34, Issue 2 https://doi.org/10.1137/S0097539794273368	journal	April 1997
Discrete Conservation Properties of Unstructured Mesh Schemes Perot, J. Blair Annual Review of Fluid Mechanics, Vol. 43, Issue 1 https://doi.org/10.1146/annurev-fluid-122109-160645	journal	January 2011

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