Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

We consider the initial boundary value problem for the homogeneous time-fractional diffusion equation ∂ t u − ∆u = 0 (0 < α < 1) with initial condition u(x, 0) = v(x) and a homogeneous Dirichlet boundary condition in a bounded polygonal domain Ω. We shall study two semidiscrete approximation schemes, i.e., Galerkin FEM and lumped mass Galerkin FEM, by using piecewise linear functions. We establ...

Pointwise localized error estimates for parabolic finite element equations

Error Estimates for the Finite Volume Element Method for Parabolic Equations in Convex Polygonal Domains

We analyze the spatially semidiscrete piecewise linear finite volume element method for parabolic equations in a convex polygonal domain in the plane. Our approach is based on the properties of the standard finite element Ritz projection and also of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite volume element method. Because the d...

Some New Error Estimates of a Semidiscrete Finite Volume Element Method for Parabolic Integro-differential Equation with Nonsmooth Initial Data

A semidiscrete finite volume element(FVE) approximation to parabolic integrodifferential equation(PIDE) is analyzed in a two-dimensional convex polygonal domain. Optimal order L-error estimates are derived for both smooth and nonsmooth initial data. More precisely, for homogeneous equations, an elementary energy technique and duality argument is used to derive optimal L-error estimate of order ...

A High Order Finite Dierence Method for Random Parabolic Partial Dierential Equations

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...