A probabilistic approach is developed for the exact solution u to a deterministic partial differential equation as well its associated approximation uh(k) performed by Pk Lagrange finite element. Two limitations motivated our approach: On one hand, inability determine relative given (which initially motivates approximating it) and, on other existence of uncertainties with numerical uh(k). We, t...

We investigate the impact of relativistic effects on upper hybrid (UH) waves in plasmas with thermal electrons, particularly focusing modifications conditions under which UH wave trapping and related low-threshold parametric decay instabilities (PDIs) may occur. A moderately (MR) dispersion relation for waves, valid electron temperatures up to 25 keV frequencies twice cyclotron frequency, is ob...

The Virtual Learning Environment (VLE) at the University of Hertfordshire (UH) not only supports institutional and national strategies in learning and teaching, but represents a significant investment in capital. Studies show that VLEs offer a variety of pedagogical benefits and usage of such systems can be effectively measured through the analysis of a system’s log files. However, although the...

In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the homogeneous Dirichlet problem for −∆u = g in Ω, our variables are i) an approximation ψh of u on the skeleton (the union of the interfaces of the sub-domains) on an independent grid (that could often be uniform), and ii) the approximations uh of u in ea...

Speech disfluencies occur frequently in spontaneous speech but their source is unclear. Disfluencies can take several forms, most commonly as verbalized disfluencies such as “um”, “uh”, and “so”, as well as silent pauses. In the present exploratory study we examined the relationship between disfluencies as distinct entities, individual differences in working memory capacity, and linguistic mark...

We propose a simple stopping criterion for the conjugate gradient (CG) algorithm in the framework of anisotropic, adaptive finite elements for elliptic problems. The goal of the adaptive algorithm is to find a triangulation such that the estimated relative error is close to a given tolerance TOL. We propose to stop the CG algorithm whenever the residual vector has Euclidian norm less than a sma...

Self-dual 1-configurations (nd)1 have the most Kd-separated Menger graph Y for connected self-dual configurations (nd). Such Y is most symmetric if it is Kd-ultrahomogeneous. In this work, such a graph Y is presented for (n, d) = (102, 4) and shown to relate n copies of the cuboctahedral graph L(Q3) to the n copies of K4. These are shown to share each copy of K3 with two copies of L(Q3). Vertic...

In this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane. We introduce a general approach for connecting these methods with finite element method analysis. This unified approach is used to prove known convergence results in the H1, L2 norms and new results in the max-norm. For the elliptic ...