Guaranteed error control bounds for the stabilised space-time IgA approximations to parabolic problems

12/16/2017

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by   Ulrich Langer, et al.

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The paper is concerned with space-time IgA approximations of parabolic initial-boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of IgA approximations and investigate their applicability. The derivation method is based on the analysis of respective integral identities and purely functional arguments. Therefore, the estimates do not contain mesh-dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply computable error bounds for norms associated with stabilised space--time IgA approximations. The last section of the paper contains a series of numerical examples where approximate solutions are recovered by IgA techniques. They illustrate reliability and efficiency of the error estimates presented.