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In this paper a time-splitting technique for the two dimensional advectiondispersion equation is proposed. A high resolution in space Godunov method for advection is combined with the RT0 Mixed Finite Element for the discretization of the dispersion term. Numerical tests on an analytical one dimensional example ascertain the convergence properties of the scheme. At di erent Peclet numbers, the choice of optimal time step size used for the two equations is discussed, showing that with accurate selection of the time step sizes, the overall CPU time required by the simulations can be drastically reduced. Results on a realistic test case of groundwater contaminant transport con rm that the proposed scheme does not su er from Peclet limitations, and always displays only small amounts of numerical di usion across the entire range of Peclet numbers.

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The meshless local Petrov-Galerkin (MLPG) method is a meshfree procedure for solving partial differential equations. However, the benefit in avoiding the mesh construction and refinement is counterbalanced by the use of complicated non polynomial shape functions with subsequent difficulties, and a potentially large cost, when implementing numerical integration schemes. In this paper we describe and compare some numerical quadrature rules with the aim at preserving the MLPG solution accuracy and at the same time reducing its computational cost.

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