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Mathematics of Computation

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A Galerkin method for the forward-backward heat equation


Authors: A. K. Aziz and J.-L. Liu
Journal: Math. Comp. 56 (1991), 35-44
MSC: Primary 65M60
DOI: https://doi.org/10.1090/S0025-5718-1991-1052085-2
MathSciNet review: 1052085
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Abstract: In this paper a new variational method is proposed for the numerical approximation of the solution of the forward-backward heat equation. The approach consists of first reducing the second-order problem to an equivalent first-order system, and then using a finite element procedure with continuous elements in both space and time for the numerical approximation. Under suitable regularity assumptions, error estimates and the results of some numerical experiments are presented.


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DOI: https://doi.org/10.1090/S0025-5718-1991-1052085-2
Keywords: Finite element, first-order system, error estimates
Article copyright: © Copyright 1991 American Mathematical Society