Simulation of the phase field Cahn-Hilliard and tumor growth models via a numerical scheme: Element-free Galerkin method

摘要

The main aim of this research work is to find the numerical solution based on a meshless technique for both the time-dependent Cahn-Hilliard and tumor growth partial differential equations. The temporal variable is discretized using a second-order method based on semi-implicit backward differential formula, and the stabilized term is added to the considered time discretization. Also, an adaptive time algorithm is used to reduce the number of iterations of the proposed time discretization. Besides, to approximate the spatial variables, the element-free Galerkin method is considered for both mathematical models. The result of full discrete schemes in studied models is solved via Biconjugate gradient stabilized algorithm. Some numerical simulations are reported to show the capability of the numerical scheme presented here. (C) 2018 Elsevier B.V. All rights reserved.