26 research outputs found
Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient
We couple the L1 discretization of the Caputo fractional derivative in time
with the Galerkin scheme to devise a linear numerical method for the semilinear
subdiffusion equation. Two important points that we make are: nonsmooth initial
data and time-dependent diffusion coefficient. We prove the stability and
convergence of the method under weak assumptions concerning regularity of the
diffusivity. We find optimal pointwise in space and global in time errors,
which are verified with several numerical experiments
L1 scheme for solving an inverse problem subject to a fractional diffusion equation
This paper considers the temporal discretization of an inverse problem
subject to a time fractional diffusion equation. Firstly, the convergence of
the L1 scheme is established with an arbitrary sectorial operator of spectral
angle , that is the resolvent set of this operator contains for some . The relationship between the time fractional order
and the constants in the error estimates is precisely
characterized, revealing that the L1 scheme is robust as approaches
. Then an inverse problem of a fractional diffusion equation is analyzed,
and the convergence analysis of a temporal discretization of this inverse
problem is given. Finally, numerical results are provided to confirm the
theoretical results