In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed Paola F. Antonietti has been partially supported by SIR (Scientific Independence of young Researchers) starting grant n. RBSI14VT0S "PolyPDEs: Non-conforming polyhedral finite element methods for the approximation of partial differential equations" funded by the Italian Ministry

We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the granularity of the grid and the number of levels. The dependence of the convergence rate on the polynomial approximation degree p is also tracked, showing that the contraction factor of the scheme deteriorates with increasing p. A discussion on the effects of employing inherited or non-inherited sublevel solvers is also presented. Numerical experiments confirm the theoretical results.

In this paper we design and analyze a uniform preconditioner for a class of high-order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high-order conforming subspace and results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the discretization parameters, i.e., the mesh size, the polynomial degree and the penalization coefficient. The theoretical estimates obtained are supported by numerical tests

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Solid-phase microextraction (SPME) via on-fiber derivatization with O-(2,3,4,5,6-pentafluorobenzyl)-hydroxylamine (PFBHA) and gas chromatographic determination is considered a technique of choice in many analytical fields for formaldehyde (FA) monitoring. Vapor phase adsorption models of experimentally loaded PFBHA on porous divinylbenzene (DVB) SPME were investigated at 60 °C, 35 cm s-1 of air velocity, in a 1-64 min range: with the fiber completely exposed, loaded PFBHA was about 276 µg. Among the models tested, i.e. heat transfer, pseudo-second-order (PSO), Elovich, intra-particle diffusion, extra-particle diffusion and Langmuir, PFBHA adsorption was best fit by the PSO model, showing agreement with experimental data (272 µg). The sampling rate of FA in our conditions, obtained with a permeation tube system, was in agreement with literature (17.4 and 18.3 mL min-1, respectively). Thus, an overall standardization of the sampling phase is presented, leaving the sampling time as the most crucial parameter to be set for future applications.