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The accuracy of finite element solutions of Stokes's flow with strongly varying viscosity

Moresi, Louis and Zhong, Shijie and Gurnis, Michael (1996) The accuracy of finite element solutions of Stokes's flow with strongly varying viscosity. Physics of the Earth and Planetary Interiors, 97 (1-4). pp. 83-94. ISSN 0031-9201. http://resolver.caltech.edu/CaltechAUTHORS:20130327-144439696

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Abstract

We provide benchmark comparisons of two finite element (FE) mantle convection codes, CITCOM and CONMAN, against analytic solutions for Stokes' flow for strongly varying viscosity in the horizontal and vertical directions. The two codes use a similar FE formulation but different methods for solving the resulting equations. They both obtain accurate velocity, pressure and surface topography for viscosity structures which vary rapidly over a short distance, or discontinuously. The benchmarks help determine how many elements are needed to resolve a region of, for example, a convection simulation with high viscosity gradients. The overall accuracy does not depend on the global viscosity variation but on the gradients within individual elements. As a rule of thumb, accuracy can fall below 1% when there is a viscosity variation greater than a factor of two or three in an element. For iterative solution methods, necessary in three-dimensional modelling, these guidelines are required to determine the number of iterations to perform. We discuss a penalty based technique which improves the convergence of iterative solvers for general problems in which high viscosity gradients occurs spontaneously.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/0031-9201(96)03163-9DOIArticle
http://www.sciencedirect.com/science/article/pii/0031920196031639PublisherArticle
ORCID:
AuthorORCID
Moresi, Louis0000-0003-3685-174X
Gurnis, Michael0000-0003-1704-597X
Additional Information:© 1996 Elsevier Science B.V. Received 17 October 1995; accepted 21 February 1996. This research was supported by the David and Lucille Packard Foundation and NSF Grants EAR-9496185 and EAR-9417645. This paper is Contribution 5606 of the Division of Geological and Planetary Sciences, California Institute of Technology.
Group:Seismological Laboratory
Funders:
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
NSFEAR-9496185
NSFEAR-9417645
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Caltech Division of Geological and Planetary Sciences5606
Record Number:CaltechAUTHORS:20130327-144439696
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130327-144439696
Official Citation:Louis Moresi, Shijie Zhong, Michael Gurnis, The accuracy of finite element solutions of Stokes's flow with strongly varying viscosity, Physics of the Earth and Planetary Interiors, Volume 97, Issues 1–4, October 1996, Pages 83-94, ISSN 0031-9201, 10.1016/0031-9201(96)03163-9.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37655
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Apr 2013 23:59
Last Modified:24 Oct 2017 18:45

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