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Simulation of the phase field Cahn-Hilliard and tumor growth models via a numerical scheme: element-free Galerkin method. (English) Zbl 1440.74428

Summary: 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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
92-10 Mathematical modeling or simulation for problems pertaining to biology
92C42 Systems biology, networks
37L65 Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74L15 Biomechanical solid mechanics

Software:

Matlab; DistMesh
PDFBibTeX XMLCite
Full Text: DOI

References:

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