Numerical analysis of a semilinear fractional diffusion equation

08/30/2019

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by   Binjie Li, et al.

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This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Grönwall's inequality and its discrete version are proposed. By the two inequalities, error estimates in three Sobolev norms are derived for a spatial semi-discretization and a full discretization, which are optimal with respect to the regularity of the solution. A sharp temporal error estimate on graded temporal grids is also rigorously established. In addition, the spatial accuracy O(h^2(t^-α + (1/h))) in the pointwise L^2(Ω) -norm is obtained for a spatial semi-discretization. Finally, several numerical results are provided to verify the theoretical results.