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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Continuous finite elements in space and time for the heat equation


Authors: A. K. Aziz and Peter Monk
Journal: Math. Comp. 52 (1989), 255-274
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1989-0983310-2
MathSciNet review: 983310
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Abstract: In this paper we shall analyze a new variational method for approximating the heat equation using continuous finite elements in space and time. In the special case of linear elements in time the method reduces to the Crank-Nicolson Galerkin method with time-averaged data. Using higher-order finite elements in time, we obtain a new class of time stepping methods related to collocating the standard spatial Galerkin differential equations in time at the Gauss-Legendre points. Again the data enters via suitable time averages. We present error estimates and the results of some numerical experiments.


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DOI: https://doi.org/10.1090/S0025-5718-1989-0983310-2
Keywords: Galerkin method, heat equation, error estimates
Article copyright: © Copyright 1989 American Mathematical Society