0000000000200745

AUTHOR

Ulrich Langer

0000-0003-3797-7475

showing 8 related works from this author

Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

2015

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed

Mathematical optimizationControl and OptimizationMathematicsofComputing_NUMERICALANALYSISFinite element approximations010103 numerical & computational mathematicsType (model theory)01 natural sciencesparabolic time-periodic optimal control problemsError analysisFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisNumerical testsfunctional a posteriori error estimates0101 mathematicsMathematics - Optimization and Control49N20 35Q61 65M60 65F08Mathematicsta113Time periodicta111Numerical Analysis (math.NA)State (functional analysis)Optimal controlComputer Science Applications010101 applied mathematicsOptimization and Control (math.OC)multiharmonic finite element methodsSignal ProcessingA priori and a posterioriAnalysisNumerical Functional Analysis and Optimization
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A posteriori estimates for a coupled piezoelectric model

2017

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)

Physicsa posteriori error estimatesosittaisdifferentiaaliyhtälötNumerical Analysis510: Mathematik010504 meteorology & atmospheric sciencesPiezoelectricity problemcoupled systems of partial differential equations01 natural sciencesPiezoelectricity010101 applied mathematicsCoupled systems of partial differential equationsModeling and Simulationpiezoelectricity problemApplied mathematicsA priori and a posteriorinumeerinen analyysi0101 mathematicsmatemaattiset mallitvirheanalyysiA posteriori error estimate0105 earth and related environmental sciences
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Guaranteed error control bounds for the stabilised space-time IgA approximations to parabolic problems

2017

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 provide computable error bounds for norms associated with stabilised space-time IgA approximations as well as imply efficient error indicators enhancing the performance of fully adap…

65N15 65N25 65N35F.2.1; G.1.0; G.1.2; G.1.3; G.1.8; B.2.3Computer Science - Numerical AnalysisG.1.8B.2.3FOS: MathematicsG.1.2Mathematics - Numerical AnalysisF.2.1G.1.3Numerical Analysis (math.NA)G.1.0
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Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems

2019

The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Furthermore, a p…

osittaisdifferentiaaliyhtälötominaisarvotfunctional error estimatesguaranteed error boundsadaptive space–time schemesnumeerinen analyysivirheanalyysistabilised space–time IgA schemesparabolic initial-value boundary problems
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Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems

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.

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)
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Space‐Time Isogeometric Analysis of Parabolic Diffusion Problems in Moving Spatial Domains

2019

Space timeMathematical analysisIsogeometric analysisDiffusion (business)MathematicsPAMM
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Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems

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. peerReviewed

osittaisdifferentiaaliyhtälötstabilised space-time IgA schemesfunctional error estimatesnumeerinen analyysifully-adaptive space-time schemesapproksimointivirheanalyysiComputer Science::Numerical Analysiserror control
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Guaranteed error bounds and local indicators for adaptive solvers using stabilised space–time IgA approximations to parabolic problems

2019

Abstract The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Further…

Class (set theory)Series (mathematics)Space timeContext (language use)010103 numerical & computational mathematicsType (model theory)01 natural sciencesIdentity (music)010101 applied mathematicsComputational MathematicsComputational Theory and MathematicsModeling and SimulationApplied mathematicsA priori and a posteriori0101 mathematicsEnergy (signal processing)MathematicsComputers & Mathematics with Applications
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