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Christian Merdon - One of the best experts on this subject based on the ideXlab platform.

  • Guaranteed upper bounds for the Velocity Error of pressure-robust Stokes discretisations.
    arXiv: Numerical Analysis, 2020
    Co-Authors: Philip L. Lederer, Christian Merdon
    Abstract:

    This paper improves guaranteed Error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete Velocity that is independent of the exact pressure. A Prager-Synge type result relates the Errors of divergence-free primal and $H(\operatorname{div})$-conforming dual mixed methods (for the Velocity gradient) with an equilibration constraint that needs special care when discretised. To relax the constraints on the primal and dual method, a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressure-independent guaranteed upper bounds for any pressure-robust (but not necessarily divergence-free) primal discretisation. Moreover, a provably efficient local design of the equilibrated fluxes is presented that reduces the numerical costs of the Error estimator. All theoretical findings are verified by numerical examples which also show that the efficiency indices of our novel guaranteed upper bounds for the Velocity Error are close to $1$.

  • optimal l2 Velocity Error estimate for a modified pressure robust crouzeix raviart stokes element
    Ima Journal of Numerical Analysis, 2017
    Co-Authors: Alexander Linke, Christian Merdon, Winnifried Wollner
    Abstract:

    Recently, a novel approach for the robust discretization of the incompressible Stokes equations was proposed that slightly modifies the nonconforming Crouzeix–Raviart element such that its Velocity Error becomes pressure-independent. The modification results in an O(h) consistency Error that allows straightforward proofs for the optimal convergence of the discrete energy norm of the Velocity and of the L norm of the pressure. However, though the optimal convergence of the Velocity in the L norm was observed numerically, it appeared to be nontrivial to prove. In this contribution, this gap is closed. Moreover, the dependence of the energy Error estimates on the discrete inf-sup constant is traced in detail, which shows that classical Error estimates are extremely pessimistic on domains with large aspect ratios. Numerical experiments in 2D and 3D illustrate the theoretical findings.

  • Optimal L2 Velocity Error estimate for a modified pressure-robust Crouzeix–Raviart Stokes element
    IMA Journal of Numerical Analysis, 2016
    Co-Authors: Alexander Linke, Christian Merdon, Winnifried Wollner
    Abstract:

    Recently, a novel approach for the robust discretization of the incompressible Stokes equations was proposed that slightly modifies the nonconforming Crouzeix–Raviart element such that its Velocity Error becomes pressure-independent. The modification results in an O(h) consistency Error that allows straightforward proofs for the optimal convergence of the discrete energy norm of the Velocity and of the L norm of the pressure. However, though the optimal convergence of the Velocity in the L norm was observed numerically, it appeared to be nontrivial to prove. In this contribution, this gap is closed. Moreover, the dependence of the energy Error estimates on the discrete inf-sup constant is traced in detail, which shows that classical Error estimates are extremely pessimistic on domains with large aspect ratios. Numerical experiments in 2D and 3D illustrate the theoretical findings.

  • On Velocity Errors due to irrotational forces in the Navier-Stokes momentum balance
    Journal of Computational Physics, 2016
    Co-Authors: Alexander Linke, Christian Merdon
    Abstract:

    This contribution studies the influence of the pressure on the Velocity Error in finite element discretisations of the Navier-Stokes equations. Four simple benchmark problems that are all close to real-world applications convey that the pressure can be comparably large and is not to be underestimated. In fact, the Velocity Error can be arbitrarily large in such situations. Only pressure-robust mixed finite element methods, whose Velocity Error is pressure-independent, can avoid this influence. Indeed, the presented examples show that the pressure-dependent component in Velocity Error estimates for classical mixed finite element methods is sharp. In consequence, classical mixed finite element methods are not able to simulate some classes of real-world flows, even in cases where dominant convection and turbulence do not play a role.

  • Optimal and Pressure-Independent $$L^2$$ Velocity Error Estimates for a Modified Crouzeix-Raviart Element with BDM Reconstructions
    Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 2014
    Co-Authors: Christian Brennecke, Alexander Linke, Christian Merdon, Joachim Schöberl
    Abstract:

    Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax the divergence constraint. The price to pay is that a-priori estimates for the Velocity Error become pressure-dependent, while divergence-free mixed finite elements deliver pressure-independent estimates. A recently introduced new variational crime using lowest-order Raviart-Thomas Velocity reconstructions delivers a much more robust modified Crouzeix-Raviart element, obeying an optimal pressure-independent discrete \(H^1\) Velocity estimate. Refining this approach, a more sophisticated variational crime employing the lowest-order BDM element is proposed, which also allows proving an optimal pressure-independent \(L^2\) Velocity Error. Numerical examples confirm the analytical results.

Alexander Linke - One of the best experts on this subject based on the ideXlab platform.

  • optimal l2 Velocity Error estimate for a modified pressure robust crouzeix raviart stokes element
    Ima Journal of Numerical Analysis, 2017
    Co-Authors: Alexander Linke, Christian Merdon, Winnifried Wollner
    Abstract:

    Recently, a novel approach for the robust discretization of the incompressible Stokes equations was proposed that slightly modifies the nonconforming Crouzeix–Raviart element such that its Velocity Error becomes pressure-independent. The modification results in an O(h) consistency Error that allows straightforward proofs for the optimal convergence of the discrete energy norm of the Velocity and of the L norm of the pressure. However, though the optimal convergence of the Velocity in the L norm was observed numerically, it appeared to be nontrivial to prove. In this contribution, this gap is closed. Moreover, the dependence of the energy Error estimates on the discrete inf-sup constant is traced in detail, which shows that classical Error estimates are extremely pessimistic on domains with large aspect ratios. Numerical experiments in 2D and 3D illustrate the theoretical findings.

  • Optimal L2 Velocity Error estimate for a modified pressure-robust Crouzeix–Raviart Stokes element
    IMA Journal of Numerical Analysis, 2016
    Co-Authors: Alexander Linke, Christian Merdon, Winnifried Wollner
    Abstract:

    Recently, a novel approach for the robust discretization of the incompressible Stokes equations was proposed that slightly modifies the nonconforming Crouzeix–Raviart element such that its Velocity Error becomes pressure-independent. The modification results in an O(h) consistency Error that allows straightforward proofs for the optimal convergence of the discrete energy norm of the Velocity and of the L norm of the pressure. However, though the optimal convergence of the Velocity in the L norm was observed numerically, it appeared to be nontrivial to prove. In this contribution, this gap is closed. Moreover, the dependence of the energy Error estimates on the discrete inf-sup constant is traced in detail, which shows that classical Error estimates are extremely pessimistic on domains with large aspect ratios. Numerical experiments in 2D and 3D illustrate the theoretical findings.

  • ROBUST ARBITRARY ORDER MIXED FINITE ELEMENT METHODS FOR THE INCOMPRESSIBLE STOKES EQUATIONS WITH PRESSURE INDEPENDENT Velocity ErrorS
    ESAIM: Mathematical Modelling and Numerical Analysis, 2016
    Co-Authors: Alexander Linke, Gunar Matthies, Lutz Tobiska
    Abstract:

    Standard mixed finite element methods for the incompressible Navier–Stokes equations that relax the divergence constraint are not robust against large irrotational forces in the momentum balance and the Velocity Error depends on the continuous pressure. This robustness issue can be completely cured by using divergence-free mixed finite elements which deliver pressure-independent Velocity Error estimates. However, the construction of H 1 -conforming, divergence-free mixed finite element methods is rather difficult. Instead, we present a novel approach for the construction of arbitrary order mixed finite element methods which deliver pressure-independent Velocity Errors. The approach does not change the trial functions but replaces discretely divergence-free test functions in some operators of the weak formulation by divergence-free ones. This modification is applied to inf-sup stable conforming and nonconforming mixed finite element methods of arbitrary order in two and three dimensions. Optimal estimates for the incompressible Stokes equations are proved for the H 1 and L 2 Errors of the Velocity and the L 2 Error of the pressure. Moreover, both Velocity Errors are pressure-independent, demonstrating the improved robustness. Several numerical examples illustrate the results.

  • On Velocity Errors due to irrotational forces in the Navier-Stokes momentum balance
    Journal of Computational Physics, 2016
    Co-Authors: Alexander Linke, Christian Merdon
    Abstract:

    This contribution studies the influence of the pressure on the Velocity Error in finite element discretisations of the Navier-Stokes equations. Four simple benchmark problems that are all close to real-world applications convey that the pressure can be comparably large and is not to be underestimated. In fact, the Velocity Error can be arbitrarily large in such situations. Only pressure-robust mixed finite element methods, whose Velocity Error is pressure-independent, can avoid this influence. Indeed, the presented examples show that the pressure-dependent component in Velocity Error estimates for classical mixed finite element methods is sharp. In consequence, classical mixed finite element methods are not able to simulate some classes of real-world flows, even in cases where dominant convection and turbulence do not play a role.

  • Optimal and Pressure-Independent $$L^2$$ Velocity Error Estimates for a Modified Crouzeix-Raviart Element with BDM Reconstructions
    Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 2014
    Co-Authors: Christian Brennecke, Alexander Linke, Christian Merdon, Joachim Schöberl
    Abstract:

    Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax the divergence constraint. The price to pay is that a-priori estimates for the Velocity Error become pressure-dependent, while divergence-free mixed finite elements deliver pressure-independent estimates. A recently introduced new variational crime using lowest-order Raviart-Thomas Velocity reconstructions delivers a much more robust modified Crouzeix-Raviart element, obeying an optimal pressure-independent discrete \(H^1\) Velocity estimate. Refining this approach, a more sophisticated variational crime employing the lowest-order BDM element is proposed, which also allows proving an optimal pressure-independent \(L^2\) Velocity Error. Numerical examples confirm the analytical results.

Katsuari Kamei - One of the best experts on this subject based on the ideXlab platform.

  • ICICIC (2) - A Proposal of Fuzzy Control System for Trailers Driven by Multiple Motors in Side Slipway to Launch and Pull Out Ships
    First International Conference on Innovative Computing Information and Control - Volume I (ICICIC'06), 2006
    Co-Authors: N.w. Aung, Eric W. Cooper, Y. Hoshino, Katsuari Kamei
    Abstract:

    This paper describes on a control system of multiple-motor system for a side slipway ship pulling out system using fuzzy logic control. The main control system is responsible for synchronized motion of trailers and fuzzy control system is used as a key control system for compensating a Velocity Error, rotational Error and distance Error caused by the unsynchronized motion of the trailers. A simulation system is used to evaluate the performance of the control system and five different types of common Errors are used for testing the outputs of the control system

  • a proposal of fuzzy control system for trailers driven by multiple motors in side slipway to launch and pull out ships
    International Conference on Innovative Computing Information and Control, 2006
    Co-Authors: N.w. Aung, Eric W. Cooper, Y. Hoshino, Katsuari Kamei
    Abstract:

    This paper describes on a control system of multiple-motor system for a side slipway ship pulling out system using fuzzy logic control. The main control system is responsible for synchronized motion of trailers and fuzzy control system is used as a key control system for compensating a Velocity Error, rotational Error and distance Error caused by the unsynchronized motion of the trailers. A simulation system is used to evaluate the performance of the control system and five different types of common Errors are used for testing the outputs of the control system

N.w. Aung - One of the best experts on this subject based on the ideXlab platform.

  • ICICIC (2) - A Proposal of Fuzzy Control System for Trailers Driven by Multiple Motors in Side Slipway to Launch and Pull Out Ships
    First International Conference on Innovative Computing Information and Control - Volume I (ICICIC'06), 2006
    Co-Authors: N.w. Aung, Eric W. Cooper, Y. Hoshino, Katsuari Kamei
    Abstract:

    This paper describes on a control system of multiple-motor system for a side slipway ship pulling out system using fuzzy logic control. The main control system is responsible for synchronized motion of trailers and fuzzy control system is used as a key control system for compensating a Velocity Error, rotational Error and distance Error caused by the unsynchronized motion of the trailers. A simulation system is used to evaluate the performance of the control system and five different types of common Errors are used for testing the outputs of the control system

  • a proposal of fuzzy control system for trailers driven by multiple motors in side slipway to launch and pull out ships
    International Conference on Innovative Computing Information and Control, 2006
    Co-Authors: N.w. Aung, Eric W. Cooper, Y. Hoshino, Katsuari Kamei
    Abstract:

    This paper describes on a control system of multiple-motor system for a side slipway ship pulling out system using fuzzy logic control. The main control system is responsible for synchronized motion of trailers and fuzzy control system is used as a key control system for compensating a Velocity Error, rotational Error and distance Error caused by the unsynchronized motion of the trailers. A simulation system is used to evaluate the performance of the control system and five different types of common Errors are used for testing the outputs of the control system

Sheng Shou-zhao - One of the best experts on this subject based on the ideXlab platform.

  • Compensation and Estimation of Installation Drift and Velocity Accuracy for Doppler Radar
    Computer Simulation, 2013
    Co-Authors: Sheng Shou-zhao
    Abstract:

    Velocity Error is one of the main navigation Error impact factors in system which comprises of Doppler radar,heading system and navigation computer.In order to reduce the Velocity Error and improve the navigation accuracy,a method of compensation was proposed based on the real-time estimation of installation drift angle and the Velocity accuracy.The Error model was built up after the study of the principle of Doppler radar and the analysis of the Velocity Error.Then the Error was compensated on behalf of the values of the state parameters which are attached using Kalman Filtering.The simulation results show that this method can estimate the state variables correctly,the Velocity Error is reduced and the navigation accuracy is improved whether on land or at sea under normal flight conditions with some maneuvers.