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Publisher: Amsterdam [u.a.] : Elsevier Science × WGL Institute: WIAS ×

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Now showing 1 - 3 of 3
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    Ground reaction forces and external hip joint moments predict in vivo hip contact forces during gait
    (Amsterdam [u.a.] : Elsevier Science, 2022) Alves, Sónia A.; Polzehl, Jörg; Brisson, Nicholas M.; Bender, Alwina; Agres, Alison N.; Damm, Philipp; Duda, Georg N.
    Younger patients increasingly receive total hip arthroplasty (THA) as therapy for end-stage osteoarthritis. To maintain the long-term success of THA in such patients, avoiding extremely high hip loads, i.e., in vivo hip contact force (HCF), is considered essential. However, in vivo HCFs are difficult to determine and their direct measurement is limited to instrumented joint implants. It remains unclear whether external measurements of ground reaction forces (GRFs), a non-invasive, markerless and clinic-friendly measure can estimate in vivo HCFs. Using data from eight patients with instrumented hip implants, this study determined whether GRF time series data, alone or combined with other scalar variables such as hip joint moments (HJMs) and lean muscle volume (LMV), could predict the resultant HCF (rHCF) impulse using a functional linear modeling approach. Overall, single GRF time series data did not predict in vivo rHCF impulses. However, when GRF time series data were combined with LMV of the gluteus medius or sagittal HJM using a functional linear modeling approach, the in vivo rHCF impulse could be predicted from external measures only. Accordingly, this approach can predict in vivo rHCF impulses, and thus provide patients with useful insight regarding their gait behavior to avoid hip joint overloading.
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    High order discretization methods for spatial-dependent epidemic models
    (Amsterdam [u.a.] : Elsevier Science, 2022) Takács, Bálint; Hadjimichael, Yiannis
    In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size of the populations differs in space. The use of local spatial dependence yields a system of partial-differential equations with integral terms. The uniqueness and qualitative properties of the continuous model are analyzed. Furthermore, different spatial and temporal discretizations are employed, and step-size restrictions for the discrete model’s positivity, monotonicity preservation, and population conservation are investigated. We provide sufficient conditions under which high-order numerical schemes preserve the stability of the computational process and provide sufficiently accurate numerical approximations. Computational experiments verify the convergence and accuracy of the numerical methods.
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    On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows
    (Amsterdam [u.a.] : Elsevier Science, 2021) García-Archilla, Bosco; John, Volker; Novo, Julia
    The kinetic energy of a flow is proportional to the square of the norm of the velocity. Given a sufficient regular velocity field and a velocity finite element space with polynomials of degree , then the best approximation error in is of order . In this survey, the available finite element error analysis for the velocity error in is reviewed, where is a final time. Since in practice the case of small viscosity coefficients or dominant convection is of particular interest, which may result in turbulent flows, robust error estimates are considered, i.e., estimates where the constant in the error bound does not depend on inverse powers of the viscosity coefficient. Methods for which robust estimates can be derived enable stable flow simulations for small viscosity coefficients on comparatively coarse grids, which is often the situation encountered in practice. To introduce stabilization techniques for the convection-dominated regime and tools used in the error analysis, evolutionary linear convection–diffusion equations are studied at the beginning. The main part of this survey considers robust finite element methods for the incompressible Navier–Stokes equations of order , , and for the velocity error in . All these methods are discussed in detail. In particular, a sketch of the proof for the error bound is given that explains the estimate of important terms which determine finally the order of convergence. Among them, there are methods for inf–sup stable pairs of finite element spaces as well as for pressure-stabilized discretizations. Numerical studies support the analytic results for several of these methods. In addition, methods are surveyed that behave in a robust way but for which only a non-robust error analysis is available. The conclusion of this survey is that the problem of whether or not there is a robust method with optimal convergence order for the kinetic energy is still open.