PARAMETER-UNIFORM FINITE ELEMENT METHOD FOR TWO-PARAMETER SINGULARLY PERTURBED PARABOLIC REACTION-DIFFUSION PROBLEMS
2012 ◽
Vol 09
(04)
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pp. 1250047
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Keyword(s):
In this paper, parameter-uniform numerical methods for a class of singularly perturbed one-dimensional parabolic reaction-diffusion problems with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and finite element method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O(N-2( ln N)2 + Δt). Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
1983 ◽
Vol 40
(161)
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pp. 47-47
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2012 ◽
Vol 50
(5)
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pp. 2729-2743
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Keyword(s):
2021 ◽
Vol 185
◽
pp. 486-496
Keyword(s):
2015 ◽
Vol 93
(7)
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pp. 1200-1211
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Keyword(s):
2002 ◽
Vol 19
(1)
◽
pp. 89-111
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2003 ◽
Vol 19
(1)
◽
pp. 25-30
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Keyword(s):
2019 ◽
Vol 36
(2)
◽
pp. 213-227
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2004 ◽
Vol 195
(2)
◽
pp. 773-789
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A robust finite element method for a singularly perturbed elliptic problem with two small parameters
1998 ◽
Vol 36
(7)
◽
pp. 91-110
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Keyword(s):