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Media type:
E-Article
Title:
Analytical and Numerical Study of a Model of Erosion and Sedimentation
Contributor:
Eymard, Robert;
Gallouët, Thierry
Published:
Society for Industrial and Applied Mathematics, 2006
Published in:
SIAM Journal on Numerical Analysis, 43 (2006) 6, Seite 2344-2370
Language:
English
ISSN:
0036-1429
Origination:
Footnote:
Description:
<p>We consider the following problem, arising within a geological model of sedimentationerosion: For a given vector field g and a given nonnegative function F defined on a one-or twodimensional domain Ω, find a vector field under the form g̃ = ug, with 0 ≤ u(x) ≤ 1 for a.e. x ϵ Ω, such that divg̃+ F ≥ 0 and (u-1)(divg̃+ F) = 0 in Ω. We first give a weak formulation of this problem, and we prove a comparison principle on a weak solution of the problem. Thanks to this property, we get the proof of the uniqueness of the weak solution. The existence of a solution results from the proof of the convergence of an original scheme. Numerical examples show the efficiency of this scheme and illustrate its convergence properties.</p>