We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the both extra stress and the heat flux’s vector are considered. Based on such a formulation, a dual mixed finite element is constructed and analyzed. This finite element method enables us to obtain precise approximations of the dual variable which are, for the non-isothermal fluid flow problems, the viscous and poly...

In mixed-criticality systems, applications of different criticality levels share the same computing platform. To avoid spatial and temporal interference of the applications, the computing platform must implement measures for spatial and temporal isolation. In this paper we show how the enhancement of a static memory arbiter by a second, dynamic arbitration layer facilitates the interference-fre...

A significant difference between the reported volumes delivered by a fluid-filled automated liquid-handling system with eight stainless steel fixed tips was observed when a gravimetric method and a dual dye photometric method were used to measure delivered volumes between 20 and 200 microL. A series of experiments, using the default pipetting parameters, was performed which demonstrated that th...

In this paper we analyze a new dual mixed formulation of the elastodynamic system in polygonal domains. In this formulation the symmetry of the strain tensor is relaxed by the rotational of the displacement. For the time discretization of this new dual mixed formulation, we use an explicit scheme. After the analysis of stability of the fully discrete scheme, L∞ in time, L2 in space a priori err...

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is e...

Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space. These are shown to yield characterizations of the dual mixed volume, the fundamental concept in the dual Brunn-Minkowski theory. The characterizations are shown to be best possible in the sense that none of t...

For Stokes problem, we show how to obtain nite volume schemes from a Mixed nite element method with a well chosen numerical integration diagonalising the mass matrix. The analysis of the corresponding nite volume scheme is directly deduced from general results of mixed nite element theory. In this note, we exhibit nite volume scheme for Stokes problem and give optimal a priori error estimate. R...

We designed a new volume-conservative interface reconstruction method. An input data set for the interface reconstruction algorithm consists of volumes and centroids of the cell fractions occupied by different materials. Compared to pure volume fractions, traditionally used by volume-of-fluid (VoF) methods, this choice of the input data allows to define a linear interface approximation per mixe...

Some Orlicz-Brunn-Minkowski type inequalities for (dual) quermassintegrals of polar bodies and star dual have been introduced. In this paper, we generalize the results establish some mixed bodies.