On Preservation of Positivity in Some Finite Element Methods for the Heat Equation
2015 ◽
Vol 15
(4)
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pp. 417-437
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Keyword(s):
AbstractWe consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We complement in a number of ways earlier studies of the possible extension of this fact to spatially semidiscrete and fully discrete piecewise linear finite element discretizations, based on the standard Galerkin method, the lumped mass method, and the finite volume element method. We also provide numerical examples that illustrate our findings.
1985 ◽
Vol 26
(3)
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pp. 329-354
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2003 ◽
Vol 3
(1)
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pp. 45-58
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1995 ◽
Vol 05
(03)
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pp. 351-365
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2013 ◽
Vol 5
(04)
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pp. 548-568
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2016 ◽
Vol 103
(1)
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pp. 23-37
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2018 ◽
Vol 28
(06)
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pp. 1199-1231
1970 ◽
Vol 24
(109)
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pp. 31-31
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1971 ◽
Vol 29
(2)
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pp. 261-268
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