A second-order time-accurate, linear fully decoupled unconditional energy stabilization finite element method for tumor growth model

By using the $L^2$ gradient flow method, we derive a phase-field model for tumor growth from the free energy. The scalar auxiliary variable (SAV) method is employed to handle the nonlinear energy potential. Based on the second-order backward differentiation formula (BDF2) and the finite element method, we construct an unconditionally stable, linear, and decoupled fully discrete numerical scheme. We rigorously prove the unconditional energy stability of the proposed scheme and the optimal $L^2$-norm error estimates for ϕ and c. Numerical examples are presented to validate the theoretical results and to demonstrate the effectiveness of the model and the scheme.