Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise

We consider an initial- and Dirichlet boundary- value problem for a linear Cahn-Hilliard-Cook equation, in one space dimension, forced by the space derivative of a space-time white noise. First, we propose an approximate regularized stochastic parabolic problem discretizing the noise using linear splines. Then fully-discrete approximations to the solution of the regularized problem are constructed using, for the discretization in space, a Galerkin finite element method based on $H^2-$piecewise polynomials, and, for time-stepping, the Backward Euler method. Finally, we derive strong a priori estimates for the modeling error and for the numerical approximation error to the solution of the regularized problem

On the Optimal Taxation of Common-Pool Resources

Recent research developments in common-pool resource models emphasize the importance of links with ecological systems and the presence of non-linearities, thresholds and multiple steady states. In a recent paper Kossioris et al. (2008) develop a methodology for deriving feedback Nash equilibria for non-linear differential games and apply this methodology to a common-pool resource model of a lake where pollution corresponds to benefits and at the same time affects the ecosystem services. This paper studies the structure of optimal state- dependent taxes that steer the combined economic-ecological system towards the trajectory of optimal management, and provides an algorithm for calculating such taxes.Differential Games, non-linear Feedback Nash Equilibria, Ecosystems, Optimal State-dependent Tax

Evaluation of WRF performance for the analysis of surface wind speeds over various Greek regions

In this study we analyze the surface wind variability over selected areas of the Greek territory by comparing a 3-Km spatial resolution simulation performed with the Weather Research and Forecasting (WRF) model for the summer months of 2013 with actual surface measurements. Daily 36hrs runs at 12 UTC were driven by FLN (1 deg x 1 deg) data for the period of 11 July 2013 to 17 July 2013. Various verification statistics such as BIAS, RMSE and DACC for wind speed and direction were used to gauge the mesoscale model performance

Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem

We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regularize the white noise and study the regularized problem, (2) approximate the regularized problem. We address (1) by introducing a piecewise constant random approximation of the white noise with respect to a space-time mesh. We analyze the regularized problem and study its relation to both the original problem and the deterministic Allen-Cahn problem. Step (2) is then performed leading to a practical Monte-Carlo method combined with a Finite Element-Implicit Euler scheme. The resulting numerical scheme is tested against theoretical benchmark results.Comment: 28 pages, 16 (4x4) figures, published in 2007; Interfaces and Free Boundaries 2007 vol. 9 (1