Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems

  • Ulrich Langer
  • Svetlana MatculevichEmail author
  • Sergey Repin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)


The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example.


Error control Functional error estimates Stabilised space-time IgA schemes Fully-adaptive space-time schemes 



The research is supported by the Austrian Science Fund (FWF) through the NFN S117-03 project. Implementation was carried out using the open-source C++ library G+smo [19] developed at RICAM.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Ulrich Langer
    • 1
  • Svetlana Matculevich
    • 1
    Email author
  • Sergey Repin
    • 2
    • 3
  1. 1.RICAM Linz, Johann Radon InstituteLinzAustria
  2. 2.St. Petersburg Department of V.A. Steklov Institute of Mathematics RASSaint PetersburgRussia
  3. 3.University of JyvaskylaJyväskyläFinland

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