1 research outputs found
Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditional energy-stable fully discrete scheme
This work is devoted to the study of a fully discrete scheme for a repulsive
chemotaxis with quadratic production model. By following the ideas presented in
[Guilen-Gonzalez et al], we introduce an auxiliary variable (the gradient of
the chemical concentration), and prove that the corresponding Finite Element
(FE) backward Euler scheme is conservative and unconditionally energy-stable.
Additionally, we also study some properties like solvability, a priori
estimates, convergence towards weak solutions and error estimates. On the other
hand, we propose two linear iterative methods to approach the nonlinear scheme:
an energy-stable Picard method and Newton's method. We prove solvability and
convergence of both methods towards the nonlinear scheme. Finally, we provide
some numerical results in agreement with our theoretical analysis with respect
to the error estimates