Abstract
In this chapter we consider an alternative to time stepping for the discretization in time of an initial value problem for a parabolic equation. We now use a representation of the solution as an integral along a smooth curve extending into the complex right half plane, with an integrand containing the resolvent of the associated elliptic operator. This integral is then evaluated to high accuracy by a quadrature rule. In this way the problem is reduced to a finite set of elliptic equations, which may be solved in parallel. The procedure is combined with finite element discretization in the spatial variables.
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© 2006 Springer
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Thomée, V. (2006). Time Discretization by Laplace Transformation and Quadrature. In: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33122-0_20
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DOI: https://doi.org/10.1007/3-540-33122-0_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33121-6
Online ISBN: 978-3-540-33122-3
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