, Volume 53, Issue 1, pp 19–34 | Cite as

On long time integration of the heat equation

  • Roman Andreev


We construct space-time Petrov–Galerkin discretizations of the heat equation on an unbounded temporal interval, either right-unbounded or left-unbounded. The discrete trial and test spaces are defined using Laguerre polynomials in time and are shown to satisfy the discrete inf-sup condition. Numerical examples are provided.


Heat equation Long-time Laguerre polynomials Stability 

Mathematics Subject Classification

35K05 65M60 65M12 



The author thanks Ch. Schwab for motivating the topic, and the anonymous referees for their helpful suggestions.


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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  1. 1.RICAMLinzAustria

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