LeapfrogFinite Element Method for Fractional Diffusion Equation

Abstract EN

We analyze a fully discrete leapfrog/Galerkin finiteelement method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation.

The generalized fractional derivative spaces aredefined in a bounded interval.

And some related properties are further discussed for thefollowing finite element analysis.

Then the fractional diffusion equationis discretized in space by the finite element method and in time by the explicitleapfrog scheme.

For the resulting fully discrete, conditionally stable scheme,we prove an L 2 -error bound of finite element accuracy and of second order intime.

Numerical examples are included to confirm our theoretical analysis.