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Finite element error estimates for nonlinear convective problems

  • Václav Kučera EMAIL logo


This paper is concerned with the analysis of the finite element method applied to a nonstationary nonlinear convective problem. Using special estimates of the convective terms, we prove a priori error estimates for an explicit, semidiscrete and implicit scheme. While the explicit case is rather straightforward via mathematical induction, for the semidiscrete scheme we need to apply so-called continuous mathematical induction and a nonlinear Gronwall lemma. For the implicit scheme, we use a suitable continuation of the discrete implicit solution and again use continuous mathematical induction to prove the error estimates. Finally, we extend the presented analysis from globally Lipschitz-continuous convective nonlinearities to the locally Lipschitz-continuous case.

MSC 2010: 65M15; 65M60; 65M12


This work is a part of the research projects P201/11/P414 and P201/13/00522S of the Czech Science Foundation. V. Kucera is a junior researcher at the University Center for Mathematical Modelling, Applied Analysis and Computational Mathematics (Math MAC).


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Received: 2015-3-9
Revised: 2015-9-14
Accepted: 2015-10-9
Published Online: 2016-10-5
Published in Print: 2016-10-1

© 2016 Walter de Gruyter GmbH, Berlin/Boston

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