Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems
Langer, U., Matculevich, S., & Repin, S. (2018). Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems. In I. Lirkov, & S. Margenov (Eds.), LSSC 2017 : Large-Scale Scientific Computing, 11th International Conference. Revised Selected Papers (pp. 55-65). Lecture Notes in Computer Science, 10665. Cham: Springer International Publishing. doi:10.1007/978-3-319-73441-5_5
Published inLecture Notes in Computer Science
© Springer International Publishing AG 2018.
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.