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Explicit Adaptive Fup Collocation Method for solving the parabolic problems

In this paper we will present meshless Adaptive Fup Collocation Method (AFCM) based on Fup basis functions and collocation approach for spatial approximation [2] and explicit stabilized Runge-Kutta temporal integration especially well suited for stiff parabolic problems [3]. The basic scheme of MOL methodology was described in [2], but now we improve efficiency of the spatial approximation, introduce a novel explicit time integration scheme and therefore significantly increase capabilities of the methodology for a real demanding 2-D and 3-D stiff parabolic problems. On the other side, we implement stabilized Runge–Kutta methods (they have also been called Chebyshev–Runge–Kutta methods) which are explicit methods with extended stability domains, usually along the negative real axis. Due to demonstrative purposes, we present the efficiency of the AFCM to the Henry saltwater benchmark example of groundwater density driven flow.

Explicit integration; Fup basis function; adaptive algortithm; parabolic problems

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