An expanded mixed finite element simulation for two-sided time-dependent fractional diffusion problem

An expanded mixed finite element simulation for two-sided time-dependent fractional diffusion problem

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Abstract In this paper, we consider a time-dependent diffusion problem with two-sided Riemann-Liouville fractional derivatives.By introducing a fractional-order flux as auxiliary variable, we establish the saddle-point variational formulation, based on which we employ a locally conservative mixed finite element method to approximate NN@5 the unknown function, its derivative and the fractional flux in space and use the backward Euler scheme to discrete the time Plush Toys derivative, and thus propose a fully discrete expanded mixed finite element procedure.We prove the well-posedness and the optimal order error estimates of the proposed procedure for a sufficiently smooth solution.Numerical experiments are presented to confirm our theoretical findings.