相关论文: Description of random level sets by polynomial cha…
One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic structure, and the stochastic energy increases linearly in time.…
We present a computational study of several preconditioning techniques for the GMRES algorithm applied to the stochastic diffusion equation with a lognormal coefficient discretized with the stochastic Galerkin method. The clear block…
An exact analytical method for determining the Lagrangian velocity correlation and the diffusion coefficient for particles moving in a stochastic velocity field is derived. It applies to divergence-free 2-dimensional Gaussian stochastic…
The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the velocity in the L$^2$ norm in time and in space.…
In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…
This paper presents heavily grad-div and pressure jump stabilised, equal- and mixed-order discontinuous Galerkin finite element methods for non-isothermal incompressible flows based on the Oberbeck-Boussinesq approximation. In this…
We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic…
We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence results and error bounds are obtained for mapped tent pitching…
Jump penalty stabilisation techniques have been recently proposed for continuous and discontinuous high order Galerkin schemes [1,2,3]. The stabilisation relies on the gradient or solution discontinuity at element interfaces to incorporate…
We consider the nearly incompressible linear elasticity problem with an uncertain spatially varying Young's modulus. The uncertainty is modelled with a finite set of parameters with prescribed probability distribution. We introduce a novel…
Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast…
We consider linear hyperbolic balance law that describe gas flow. Stochastic influences are introduced by series of orthogonal functions. A deterministic stabilization concept, which makes deviations at steady states decay exponentially…
We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and…
We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization…