Abstract. In this paper, we present a shock capturing discontinuous Galerkin (SC-DG) method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time formulation in terms of entropy variables using an entropy stable numerical flux. While being similar to the method proposed in [14], our approach is ne...

Geographically weighted regression (GWR) is a way of exploring spatial nonstationarity by calibrating a multiple regression model which allows different relationships to exist at different points in space. Nevertheless, formal testing procedures for spatial nonstationarity have not been developed since the inception of the model. In this paper the authors focus mainly on the development of stat...

Diffusion MRI allows us to make inferences on the structural organisation of the brain by mapping water diffusion to white matter microstructure. However, such a mapping is generally ill-defined; for instance, diffusion measurements are antipodally symmetric (diffusion along x and -x are equal), whereas the distribution of fibre orientations within a voxel is generally not symmetric. Therefore,...

We extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shockcapturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the mesh size. With this term present, we prove a maximum norm bound for finite element solutions of Burgers' equation and t...

History matching large reservoir models under a realistic geological continuity constraint remains an outstanding problem. We propose a new combined geostatistical and streamline-based method potentially capable of history matching large reservoir models, while accounting consistently for geological continuity as provided by a permeability histogram and variogram, and production data. While mos...