Galerkin Spectral Method of Stochastic Partial Differential Equations ...

2.1. Stochastic Galerkin Spectral Method · (i) · where the polynomial chaos orthogonal basis set will be constructed in the next section. · (ii).

Our novel numerical method is applied to solve the one- and two-dimensional stochastic Poisson equations, as well as the one and two-dimensional ...

Galerkin Spectral Method of Stochastic Partial Differential Equations ...

Our novel numerical method is applied to solve the one- and two-dimensional stochastic Poisson equations, as well as the one and two-dimensional stochastic heat ...

Research Article Galerkin Spectral Method of Stochastic Partial ...

Sec- ond, we apply the stochastic Galerkin method to derive deterministic differential equations for the coefficients of the expansion. Tird, we employ a ...

Solution of stochastic partial differential equations using Galerkin ...

It is worthwhile to mention our approach when adaptive finite element methods are used, has a clear relation to an adapative Monte Carlo Method. Various ...

A fast discrete spectral method for stochastic partial differential ...

The goal of this paper is to construct an efficient numerical algorithm for computing the coefficient matrix and the right hand side of the ...

[Retracted] Efficient Stochastic Galerkin Spectral Methods for ...

For the numerical approximation, we use the stochastic Galerkin spectral methods, which apply the stochastic Galerkin method for the ...

Reduced basis stochastic Galerkin methods for partial differential ...

We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis ...

Stochastic Spectral Galerkin and Collocation Methods for PDEs with ...

Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty ...

Galerkin Finite Element Methods for Stochastic Parabolic Partial ...

We study the finite element method for stochastic parabolic partial differential equations driven by nuclear or space-time white noise in the ...

Spectral Element Methods for Stochastic Differential Equations with ...

studied spectral Galerkin method for stochastic wave equations ... Yan, Finite element methods for semilinear elliptic stochastic partial differential equations, ...

A fast discrete spectral method for stochastic partial differential...

... linear system resulting from the spectral Galerkin approximation of a stochastic elliptic partial differential equation. We establish that ...

On the convergence of the stochastic Galerkin method for random ...

Mugler, Antje, and Starkloff, Hans-Jörg. "On the convergence of the stochastic Galerkin method for random elliptic partial differential equations.

Optimal Error Estimates of Galerkin Finite Element Methods ... - arXiv

Abstract:We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative ...

Spectral Method for Nonlinear Stochastic Partial Differential ...

This paper is concerned with the numerical approximations of semi-linear stochastic partial differential equations of elliptic type in multi-dimensions. Conver-.

Spectral Methods for Multiscale Stochastic Differential Equations

multiscale method (HMM) [62, 21, 1] and the equation-free approach [36]. In particular, the. PDE-based formulas (4) are replaced by Green–Kubo-type formulas [21 ...

Stochastic finite element methods for partial differential equations ...

Stochastic finite element methods refer to an extensive class of algorithms for the approximate solution of partial differential equations having random input ...

Numerical methods for deterministic and stochastic fractional partial ...

The approximated stochastic space fractional partial differential equation is then solved by using Fourier spectral methods. Thirdly, we will consider the ...

Convergence of the Spectral Method for Stochastic Ginzburg ...

Keywords: spectral method, Ginzburg-Landau equation, stochastic partial differential equa- ... The finite difference and finite element methods for equations ...

On the convergence of the stochastic Galerkin method for random ...

On the convergence of the stochastic Galerkin method for random elliptic partial differential equations ... Mathematisches Institut, ...