Error estimates for a semidiscrete finite element method for fractional order parabolic equations

Details 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

2012-04-17

arxiv.org/abs/1204.3884v1

Mathematics

Numerical Analysis

29 pages, 3 figures

Scientific paper

We consider the initial boundary value problem for the homogeneous time-fractional diffusion equation $\partial^\alpha_t u - \De u =0$ ($0< \alpha < 1$) with initial condition $u(x,0)=v(x)$ and a homogeneous Dirichlet boundary condition in a bounded polygonal domain $\Omega$. We shall study two semidiscrete approximation schemes, i.e., Galerkin FEM and lumped mass Galerkin FEM, by using piecewise linear functions. We establish optimal with respect to the regularity of the solution error estimates, including the case of nonsmooth initial data, i.e., $v \in L_2(\Omega)$.

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