Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …

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 …

The Euler equations subject to uncertainty in the initial and boundary conditions are
investigated via the stochastic Galerkin approach. We present a new fully intrusive method …

Polynomial Chaos (PC) based intrusive methods for uncertainty quantification reformulate
the original deterministic model equations to obtain a system of equations for the PC …

In this paper, we present a Bayesian framework for estimating joint densities for large eddy
simulation (LES) sub‐grid scale model parameters based on canonical forced isotropic …

The objective of this work is to investigate the efficacy of using calibration strategies from
Uncertainty Quantification (UQ) to determine model coefficients for LES. As the target …

Using Burgers' equation with mixed Neumann–Dirichlet boundary conditions, we highlight a
problem that can arise in the numerical approximation of nonlinear dynamical systems on …

Conservation laws with uncertain initial and boundary conditions are approximated using a
generalized polynomial chaos expansion approach where the solution is represented as a …

The Euler equations subject to uncertainty in the input parameters are investigated via the
stochastic Galerkin approach. We present a new fully intrusive method based on a variable …

In this chapter we demonstrate how to apply the methods we presented in the previous
chapters to stochastic nonlinear conservations laws. Specifically, since the problem is …