Abstract
A linearized decoupled Crank–Nicolson (CN) fully discrete scheme is developed by Galerkin FEM for a class of chemotactic models with nonlinear secretion. The scheme can reduce the dimension of the coefficient matrix greatly in numerical simulation compared with the implicit schemes. The existence and uniqueness of the numerical solutions are proved, and the unconditional superclose results in H1-norm are derived through rigorous theoretical analysis. It shows that the scheme can be calculated with large time step, which has incomparable advantages for the long time simulation of the model. Then, by interpolation post-processing technology, the superconvergence result is obtained. In addition, some other popular finite elements are discussed for solving the model. Finally, the numerical results are also provided to testify the theoretical analysis.
Published Version
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