Investigating the Fracture of BSCF Material with the Extended Drucker–Prager Model Through Finite Element Simulations

Patra, Sankar Narayan; Sikder, Bablu; Chanda, Abhra

doi:10.1007/s40819-020-0776-y

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2021

2023

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Cited by 2 publications

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“…These finite element functions are chosen to be simple enough to allow for efficient computation and yet provide a good approximation to the true solution. Recently, the Galerkin finite element method was used to solve various problems, and the accuracy and convergence of the method were analyzed, see, for example, [9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model

Almusawi

Harfash

2023

Preprint

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In this article, the finite element approximation of the two-species Shigesada-Kawasaki-Teramoto model, with cross-diffusion for one species, is studied. In the beginning, the regularized problem of the model and the entropy proof of the regularized problem were presented. Also, an approxi- mation of the regularized problem using the finite element method was introduced. A number of bounds were found in different spaces for approximate solutions. In addition, depending on the bounds that are obtained, the convergence of the approximate problem to the weak form of the problem was studied, and thus the existence of solutions to the Shigesada-Kawasaki-Teramoto model was proved. Also, a practical algorithm for solving the approximate problem was presented and used to calculate the numerical results of the problem.

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