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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Time Discretization by Laplace Transformation and Quadrature
verfasst von : Vidar Thomée
Erschienen in: Galerkin Finite Element Methods for Parabolic Problems
Verlag: Springer Berlin Heidelberg
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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.