Search results for "a posteriori error analysis"

showing 2 items of 2 documents

Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems

2019

In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…

Optimization problemtime-periodic conditionmultiharmonic finite element methodDiscretizationtwo-sided boundsSystems and Control (eess.SY)010103 numerical & computational mathematicsSystem of linear equationsElectrical Engineering and Systems Science - Systems and Control01 natural sciencesUpper and lower boundsSaddle pointFOS: MathematicsFOS: Electrical engineering electronic engineering information engineeringApplied mathematicsMathematics - Numerical AnalysisBoundary value problem0101 mathematicsMathematics - Optimization and ControlMathematicsosittaisdifferentiaaliyhtälöt35Kxx 65M60 65M70 65M15 65K10parabolic optimal control problemsNumerical Analysis (math.NA)matemaattinen optimointiOptimal controlFinite element method010101 applied mathematicsComputational MathematicsComputational Theory and MathematicsOptimization and Control (math.OC)Modeling and Simulationa posteriori error analysisnumeerinen analyysiguaranteed lower boundsComputers & Mathematics with Applications
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A posteriori error estimates for Webster's equation in wave propagation

2015

We consider a generalised Webster’s equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster’s equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique. peerReviewed

Wave propagationWave propagationApplied MathematicsMathematical analysista111Tubular domainDynamical Systems (math.DS)Acoustic waveWave equationPrimary 37L05. Secondary 35L05 35L20 47N70 93C20A posteriori error analysisMathematics - Analysis of PDEsApproximation errorFOS: MathematicsCalculusA priori and a posterioriWebster's modelMathematics - Dynamical SystemsAnalysisAnalysis of PDEs (math.AP)MathematicsVariable (mathematics)
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