6 research outputs found
Optimal and a posteriori error estimates for the fully discrete approximations of time fractional parabolic differential equations
We derive optimal order a posteriori error estimates in the
and -norms for the fully discrete approximations of time fractional
parabolic differential equations. For the discretization in time, we use the
methods, while for the spatial discretization, we use standard conforming
finite element methods. The linear and quadratic space-time reconstructions are
introduced, which are generalizations of the elliptic space reconstruction.
Then the related a posteriori error estimates for the linear and quadratic
space-time reconstructions play key roles in deriving global and pointwise
final error estimates. Numerical experiments verify and complement our
theoretical results.Comment: 22 page