Estimates of the Distance to Exact Solutions of the Stokes Problem with Slip and Leak Boundary Conditions

We deduce a posteriori error estimates of functional type for the stationary Stokes problem with slip and leak boundary conditions. The derived error majorants do not contain mesh dependent constants and are valid for a wide class of energy admissible approximations that satisfy the Dirichlet boundary condition on a part of the boundary. Different forms of error majorants contain global constants associated with Poincaré type inequalities or the stability (LBB) condition for the Stokes problem or constants associated with subdomains (if a domain decomposition is applied). It is proved that the majorants are guaranteed and vanish if and only if the functions entering them coincide with the r…

On the optimal cooling of the steel during continuous casting

SNAPSHOT SPECTRAL AND COLOR IMAGING USING A REGULAR DIGITAL CAMERA WITH A MONOCHROMATIC IMAGE SENSOR

Spectral imaging (SI) refers to the acquisition of the three-dimensional (3D) spectral cube of spatial and spectral data of a source object at a limited number of wavelengths in a given wavelength range. Snapshot spectral imaging (SSI) refers to the instantaneous acquisition (in a single shot) of the spectral cube, a process suitable for fast changing objects. Known SSI devices exhibit large total track length (TTL), weight and production costs and relatively low optical throughput. We present a simple SSI camera based on a regular digital camera with (i) an added diffusing and dispersing phase-only static optical element at the entrance pupil (diffuser) and (ii) tailored compressed sensing…

ℓp-solutions of countable infinite systems of equations and applications to electrical circuits

In the preceding chapter we have studied a lumped parameter model of a class of circuits containing a finite number of elements. Here we are interested in qualitative properties of the network in Figure 3.1.

A mixed finite element method for the heat flow problem

A semidiscrete finite element scheme for the approximation of the spatial temperature change field is presented. The method yields a better order of convergence than the conventional use of linear elements.