Abstract.
The Galerkin finite element method for the forward-backward heat equation is generalized to a wider class of equations with the use of a result on the existence and uniqueness of a weak solution to the problems. First, the theory for the Galerkin method is extended to forward-backward heat equations which contain additional convection and mass terms on an irregular domain. Second, variable transformations are constructed and applied to solve a wide class of forward-backward heat equations that leads to a substantial improvement. Third, Error estimates are presented. Finally, conducted numerical tests corroborate the obtained results.
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Received February 4, 1997 / Revised version received December 8, 1997
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Lu, H., Maubach, J. A finite element method and variable transformations for a forward-backward heat equation. Numer. Math. 81, 249–272 (1998). https://doi.org/10.1007/s002110050391
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DOI: https://doi.org/10.1007/s002110050391