Abstract
Space fractional advection dispersion equation includes non-local differential operators, which leads to calculating numerical integrals with weakly singular kernel on every subintervals. Oscillations are visible in computed solutions when fractional order tends to 1. Studies show that the stiffness matrix of time semi-discretization can be calculated directly by formulas established from a special variational formulation. Oscillations are eliminated by using adaptive moving mesh and De Boor algorithm, while the number of nodes remains unchanged.
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