7,487 research outputs found
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime
The numerical approximation of an inverse problem subject to the
convection--diffusion equation when diffusion dominates is studied. We derive
Carleman estimates that are on a form suitable for use in numerical analysis
and with explicit dependence on the P\'eclet number. A stabilized finite
element method is then proposed and analysed. An upper bound on the condition
number is first derived. Combining the stability estimates on the continuous
problem with the numerical stability of the method, we then obtain error
estimates in local - or -norms that are optimal with respect to the
approximation order, the problem's stability and perturbations in data. The
convergence order is the same for both norms, but the -estimate requires
an additional divergence assumption for the convective field. The theory is
illustrated in some computational examples.Comment: 21 pages, 6 figures; in v2 we added two remarks and an appendix on
psiDOs, and made some minor correction
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Suboptimal eye movements for seeing fine details.
Human eyes are never stable, even during attempts of maintaining gaze on a visual target. Considering transient response characteristics of retinal ganglion cells, a certain amount of motion of the eyes is required to efficiently encode information and to prevent neural adaptation. However, excessive motion of the eyes leads to insufficient exposure to the stimuli, which creates blur and reduces visual acuity. Normal miniature eye movements fall in between these extremes, but it is unclear if they are optimally tuned for seeing fine spatial details. We used a state-of-the-art retinal imaging technique with eye tracking to address this question. We sought to determine the optimal gain (stimulus/eye motion ratio) that corresponds to maximum performance in an orientation-discrimination task performed at the fovea. We found that miniature eye movements are tuned but may not be optimal for seeing fine spatial details
Combining Boundary-Conforming Finite Element Meshes on Moving Domains Using a Sliding Mesh Approach
For most finite element simulations, boundary-conforming meshes have
significant advantages in terms of accuracy or efficiency. This is particularly
true for complex domains. However, with increased complexity of the domain,
generating a boundary-conforming mesh becomes more difficult and time
consuming. One might therefore decide to resort to an approach where individual
boundary-conforming meshes are pieced together in a modular fashion to form a
larger domain. This paper presents a stabilized finite element formulation for
fluid and temperature equations on sliding meshes. It couples the solution
fields of multiple subdomains whose boundaries slide along each other on common
interfaces. Thus, the method allows to use highly tuned boundary-conforming
meshes for each subdomain that are only coupled at the overlapping boundary
interfaces. In contrast to standard overlapping or fictitious domain methods
the coupling is broken down to few interfaces with reduced geometric dimension.
The formulation consists of the following key ingredients: the coupling of the
solution fields on the overlapping surfaces is imposed weakly using a
stabilized version of Nitsche's method. It ensures mass and energy conservation
at the common interfaces. Additionally, we allow to impose weak Dirichlet
boundary conditions at the non-overlapping parts of the interfaces. We present
a detailed numerical study for the resulting stabilized formulation. It shows
optimal convergence behavior for both Newtonian and generalized Newtonian
material models. Simulations of flow of plastic melt inside single-screw as
well as twin-screw extruders demonstrate the applicability of the method to
complex and relevant industrial applications
Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics
This is the peer reviewed version of the following article: [Guasch, O., Sánchez-MartĂn, P., Pont, A., Baiges, J., and Codina, R. (2016) Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics. Int. J. Numer. Meth. Fluids, 82: 839–857. doi: 10.1002/fld.4243], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/fld.4243/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non-uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual-based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared-solenoidal mean flow, and for the aeolian tone generated by flow past a two-dimensional cylinder.Peer ReviewedPostprint (author's final draft
A finite element data assimilation method for the wave equation
We design a primal-dual stabilized finite element method for the numerical
approximation of a data assimilation problem subject to the acoustic wave
equation. For the forward problem, piecewise affine, continuous, finite element
functions are used for the approximation in space and backward differentiation
is used in time. Stabilizing terms are added on the discrete level. The design
of these terms is driven by numerical stability and the stability of the
continuous problem, with the objective of minimizing the computational error.
Error estimates are then derived that are optimal with respect to the
approximation properties of the numerical scheme and the stability properties
of the continuous problem. The effects of discretizing the (smooth) domain
boundary and other perturbations in data are included in the analysis.Comment: 23 page
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