The Finite Element Methods For Fractional Partial Diffrental Equation

A numerical approximation for a Caputo s tow-dimensional time-fractionaldiffusion equation with initial and boundary conditions is discussed in the paper. Apartial differential equivalent to the original problem is obtained by using arelationship between Caputo s fractional derivative and Riemann Liouville.Afterthat, semi-discretization is executed at the time direction. With the help ofGru w ald Letnikovderivative,a variational equation is deduced by approximatingthe differential operator with difference operator. The error is estimated in the α-norm sense.Then, for the finite element equation,we obtained a rectangularsubdivision on space dimension and discussed its superclose property. On the basis ofthe superclose, we can immediately have superconvergence from the superclose andimprove the precision of the solution in the whole area through we construct theinterpolation postprocessing operator in harmony with the finite element interpolationto define.