Automated FEM discretizations for the Stokes equation

Current FEM software projects have made significant advances in various automated modeling techniques. We present some of the mathematical abstractions employed by these projects that allow a user to switch between finite elements, linear solvers, mesh refinement and geometry, and weak forms with ve...

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Bibliographic Details
Published in:	BIT (Nordisk Tidskrift for Informationsbehandling) Vol. 48; no. 2; pp. 389 - 404
Main Authors:	Terrel, A.R., Scott, L.R., Knepley, M.G., Kirby, R.C.
Format:	Journal Article Conference Proceeding
Language:	English
Published:	Dordrecht Springer Netherlands 01-06-2008 Springer
Subjects:	Computational Mathematics and Numerical Analysis Exact sciences and technology Geometry Global analysis, analysis on manifolds Mathematical analysis Mathematics Mathematics and Statistics Numeric Computing Partial differential equations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds numerical methods, finite element methods, Stokes equations Finite element method Grid pattern 74S05 Stokes equation finite element methods 65Y99 Software Numerical method 35Q30. numerical methods Linear geometry Discretization method Stokes equations
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Summary:	Current FEM software projects have made significant advances in various automated modeling techniques. We present some of the mathematical abstractions employed by these projects that allow a user to switch between finite elements, linear solvers, mesh refinement and geometry, and weak forms with very few modifications to the code. To evaluate the modularity provided by one of these abstractions, namely switching finite elements, we provide a numerical study based upon the many different discretizations of the Stokes equations.
ISSN:	0006-3835 1572-9125
DOI:	10.1007/s10543-008-0178-8