This work is devoted to an inverse problem of identifying a source term
depending on both spatial and time variables in a parabolic equation from
single Cauchy data on a part of the boundary. A Crank-Nicolson Galerkin method
is applied to the least squares functional with an quadratic stabilizing
penalty term. The convergence of finite dimensional regularized approximations
to the sought source as measurement noise levels and mesh sizes approach to
zero with an appropriate regularization parameter is proved. Moreover, under a
suitable source condition, an error bound and corresponding convergence rates
are proved. Finally, several numerical experiments are presented to illustrate
the theoretical findings.Comment: Inverse source problem, Tikhonov regularization, Crank-Nicolson
Galerkin method, Source condition, Convergence rates, Ill-posedness,
Parabolic proble