6533b85efe1ef96bd12bfaac

RESEARCH PRODUCT

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

Sergey RepinSergey RepinUlrich LangerSvetlana Matculevich

subject

Class (set theory)Computer scienceReliability (computer networking)Space timeFunctional typeParabolaValue (computer science)010103 numerical & computational mathematicsComputer Science::Numerical Analysis01 natural sciences010101 applied mathematicsApplied mathematics0101 mathematicsError detection and correctionEnergy (signal processing)

description

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.

yearjournalcountryeditionlanguage
2018-01-01
https://doi.org/10.1007/978-3-319-73441-5_5