An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Pressure-induced electrical and structural anomalies in Pb(1-x)Ca(x)TiO(3) thin films grown at various oxygen pressures by chemical solution route

Lead calcium titanate (Pb(1-x)Ca(x)TiO(3) or PCT) thin films have been thermally treated under different oxygen pressures, 10, 40 and 80 bar, by using the so-called chemical solution deposition method. The structural, morphological, dielectric and ferroelectric properties were characterized by x-ray diffraction, FT-infrared and Raman spectroscopy, atomic force microscopy and polarization-electric-field hysteresis loop measurements. By annealing at a controlled pressure of around 10 and 40 bar, well-crystallized PCT thin films were successfully prepared. For the sample submitted to 80 bar, the x-ray diffraction, Fourier transformed-infrared and Raman data indicated deviation from the tetragonal symmetry. The most interesting feature in the Raman spectra is the occurrence of intense vibrational modes at frequencies of around 747 and 820 cm(-1), whose presence depends strongly on the amount of the pyrochlore phase. In addition, the Raman spectrum indicates the presence of symmetry-breaking disorder, which would be expected for an amorphous (disorder) and mixed pyrochlore-perovskite phase. During the high-pressure annealing process, the crystallinity and the grain size of the annealed film decreased. This process effectively suppressed both the dielectric and ferroelectric behaviour. Ferroelectric hysteresis loop measurements performed on these PCT films exhibited a clear decrease in the remanent polarization with increasing oxygen pressure.

Electrical transport in disordered and ordered magnetic domains under pressures and magnetic fields

Magnetic M( T, H, P) and electrical transport.( T, H, P) measurements in a strong spin-lattice-charge coupled La(0.7)Ca(0.3)MnO(3) system have been conducted. The application of H and P leads to the formation of different magnetic domain structures in the vicinity and below the polaronic-to-ferromagnetic transition temperature. The charge mobility is more sensitive to the variation of the spatial wave function overlap between Mn(3+) eg and O(2-) 2p orbitals due to the applied compacting pressure rather than the relative spin orientation between neighbouring Mn ions when the magnetic field is applied. In spite of the presence of different magnetic domain structures due to the sample history, the effect of magnetic field and pressure is less pronounced at lower temperatures on electrical transport properties.

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.