Mixed Covolume Methods for Elliptic Problems on Triangular Grids

We consider a covolume or finite volume method for a system of first-order PDEs resulting from the mixed formulation of the variable coefficient-matrix Poisson equation with the Neumann boundary condition. The system may represent either the Darcy law and the mass conservation law in anisotropic porous media flow, or Fourier law and energy conservation. The velocity and pressure are approximated by the lowest order Raviart-Thomas space on triangles. We prove its first-order optimal rate of convergence for the approximate velocities in the L2-and H(div; Q)-norms as well as for the approximate pressures in the L2-norm. Numerical experiments are included

Mixed Upwinding Covolume Methods on Rectangular Grids for Convection-diffusion Problems

We consider an upwinding covolume or control-volume method for a system of rst order PDEs resulting from the mixed formulation of a convection-di usion equation with a variable anisotropic di usion tensor. The system can be used to model the steady state of the transport of a contaminant carried by a °ow. We use the lowest order Raviart{Thomas space and show that the concentration and concentration °ux both converge at one-half order provided that the exact °ux is in H1(­)2 and the exact concentration is in H1(­). Some numerical experiments illustrating the error behavior of the scheme are provided

Piecewise linear transformation in diffusive flux discretization

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along material discontinuities using only cell concentration values. This is often resolved by introducing auxiliary node, edge, or face concentration values that are explicitly interpolated from the surrounding cell concentrations. We propose to discretize the diffusive flux after applying a local piecewise linear coordinate transformation that effectively removes the discontinuities. The resulting scheme does not need any auxiliary concentrations and is therefore remarkably simpler, while being second-order accurate under the assumption that the structure of the domain is locally layered.Comment: 11 pages, 1 figures, preprint submitted to Journal of Computational Physic

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Increased blood pressure in adult offspring of families with Balkan Endemic Nephropathy: a prospective study

BACKGROUND: Previous studies have linked smaller kidney dimensions to increased blood pressure. However, patients with Balkan Endemic Nephropathy (BEN), whose kidneys shrink during the course of the disease, do not manifest increased blood pressure. The authors evaluated the relationship between kidney cortex width, kidney length, and blood pressure in the offspring of BEN patients and controls. METHODS: 102 offspring of BEN patients and 99 control offspring of non-BEN hospital patients in the Vratza District, Bulgaria, were enrolled in a prospective study and examined twice (2003/04 and 2004/05). Kidney dimensions were determined using ultrasound, blood pressure was measured, and medical information was collected. The parental disease of BEN was categorized into three groups: mother, father, or both parents. Repeated measurements were analyzed with mixed regression models. RESULTS: In all participants, a decrease in minimal kidney cortex width of 1 mm was related to an increase in systolic blood pressure of 1.4 mm Hg (p = 0.005). There was no association between kidney length and blood pressure. A maternal history of BEN was associated with an increase in systolic blood pressure of 6.7 mm Hg (p = 0.03); paternal BEN, +3.2 mm Hg (p = 0.35); or both parents affected, +9.9 mm Hg (p = 0.002). There was a similar relation of kidney cortex width and parental history of BEN with pulse pressure; however, no association with diastolic blood pressure was found. CONCLUSION: In BEN and control offspring, a smaller kidney cortex width predisposed to higher blood pressure. Unexpectedly, a maternal history of BEN was associated with average increased systolic blood pressure in offspring