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 …

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 …

We propose a nonintrusive reduced‐order modeling method based on the notion of space‐
time‐parameter proper orthogonal decomposition (POD) for approximating the solution of …

A novel fourth-order three-point compact operator for the nonlinear convection term uux is
provided in this paper. The operator makes the numerical analysis of higher-order difference …

This paper formulates a third-order backward differentiation formula (BDF3) fourth-order
compact difference scheme based on a developed fourth-order operator for computing the …

In this paper, we consider hyperbolic systems of conservation laws subject to uncertainties
in the initial conditions and model parameters. In order to solve the underlying uncertain …

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 …

The flux reconstruction is a framework of high order semidiscretisations used for the
numerical solution of hyperbolic conservation laws. Using a reformulation of these schemes …

摘要不确定性量化(Uncertainty Quantification, UQ) 是近年来国际上热门的研究课题,
其应用领域包括水文学, 流体力学, 数据同化, 天气预测等等. 由于UQ 问题中的大量随机参数 …