Yubin Yan

Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations

We study the finite element method for stochastic parabolic partial differential equations driven by nuclear or space-time white noise in the multidimensional case. The discretization with respect to space is done by piecewise linear finite elements, and in time we apply the backward Euler method. The noise is approximated by using the generalized L2-projection operator. Optimal strong convergence error estimates in the L2 and

A finite element method for time fractional partial differential equations

\dot{H}^{-1}

GEOMETRIC ERGODICITY FOR DISSIPATIVE PARTICLE DYNAMICS

norms with respect to the spatial variable are obtained. The proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem. The computational analysis and numerical example are given.

An Algorithm for the Numerical Solution of Two-Sided Space-Fractional Partial Differential Equations

In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained. The numerical examples at the end of the paper show that the experimental results are consistent with our theoretical results.

Numerical analysis of a two-parameter fractional telegraph equation

Dissipative particle dynamics is a model of multi-phase fluid flows described by a system of stochastic differential equations. We consider the problem of N particles evolving on the one-dimensional periodic domain of length L and, if the density of particles is large, prove geometric convergence to a unique invariant measure. The proof uses minorization and drift arguments, but allows elements of the drift and diffusion matrix to have compact support, in which case hypoellipticity arguments are not directly available

Stability of a Numerical Method for a Space-time-fractional Telegraph Equation

Abstract We introduce an algorithm for solving two-sided space-fractional partial differential equations. The space-fractional derivatives we consider here are left-handed and right-handed Riemann–Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. We approximate the Hadamard finite-part integrals by using piecewise quadratic interpolation polynomials and obtain a numerical approximation of the space-fractional derivative with convergence order O(Δx 3-α )

Stabilizing Semilinear Parabolic Equations

{O(\Delta x^{3- \alpha })}

High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations

, 1<α<2

Postprocessing the Finite Element Method for Semilinear Parabolic Problems

{1<\alpha <2}

A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation

. A shifted implicit finite difference method is applied for solving the two-sided space-fractional partial differential equation and we prove that the order of convergence of the finite difference method is O(Δt+Δx min(3-α,β) )