High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …

Uncertainty quantification in computational physics is a broad research field that has spurred
increasing interest in the last two decades, partly due to the growth of computer power. The …

The non-intrusive B-splines Bézier elements method (BSBEM) is used to perform uncertainty
propagation for complex dam break flow models. The predictive efficiency of the BSBEM is …

Accurate analytical and numerical modeling of multiscale systems is a daunting task. The
need to properly resolve spatial and temporal scales spanning multiple orders of magnitude …

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is
to show that different boundary conditions give different convergence rates of the variance of …

We model random locations of spatial interfaces of heterogeneities in porous media by
means of the hybrid stochastic Galerkin (HSG) approach. This approach extends the …

A detailed description of the subsurface reservoir properties is required to make accurate
predictions of the nonlinear fluid dynamics. The combination of strong spatial heterogeneity …

Propagation of uncertainty in multidimensional dynamical systems, in the presence of
parametric uncertainties, can be quantified by the solution of the underlying Liouville …

A new scheme for the numerical approximation of a five-equation model taking into account
Uncertainty Quantification (UQ) is presented. In particular, the Discrete Equation Method …

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of
simulated responses are crucial to explore possible scenarios and assess risks in …