On mass conservation in least-squares methods

Authors:
P. Bolton;R. W. Thatcher
Affiliations:
Department of Mathematics, UMIST, Sackville Street, P.O. Box 88, Manchester M60 1QD, UK;Department of Mathematics, UMIST, Sackville Street, P.O. Box 88, Manchester M60 1QD, UK
Venue:
Journal of Computational Physics
Year:
2005

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Abstract

We compare three least-squares finite element reformulations of the Stokes equations, paying particular attention to mass conservation. The first problem we approximate has a simple analytical solution over a convex region. Even for this simple problem, without special treatment of the conservation of mass term, very poor numerical solutions may result. Sufficiently weighting this term leads to a dramatic improvement in the results over a range of test problems.