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TVD finite point method for two-dimensional conservation equation

A new meshless method, called total variation diminishing (TVD) finite point method (TVDFP), is proposed. The TVDFP method is developed on the least-square procedure which uses a global stencil of grid points and the two-dimensional (2D) TVD procedure for the approximation of fictitious interface directional fluxes. We present the accuracy of the TVDFP method and several 2D test computations.