A direct algorithm in some free boundary problems
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AbstractIn this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like one- and two- phase Stefan problem and of obstacle type. Our approach enters the category of fixed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The approximating coincidence set is explicitly computed and it converges in the Hausdorff-Pompeiu sense to the searched geometry. In the numerical examples, the algorithm has a very fast convergence and the obtained solutions (including the free boundaries) are accurate.
2015 ◽
Vol 373
(2050)
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pp. 20140275
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2006 ◽
Vol 136
(2)
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pp. 3672-3681
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2017 ◽
Vol 228
(2)
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pp. 477-493
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1970 ◽
Vol 76
(5)
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pp. 934-942
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2019 ◽
Vol 72
(10)
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pp. 2031-2062
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