| Abstract: |
| We will discuss a diffuse-interface (phase-field) model for tumor growth that takes into account nutrient consumption and chemotaxis. For this tumor growth model described by a nonlinear system consisting of a Cahn--Hilliard-type equation coupled with a reaction-diffusion equation, we constructed an efficient scheme based on the idea of the scalar auxiliary variable (SAV), which we show are not only decoupled and easy to implement, but also have the properties of mass conservation and unconditional energy stability. Furthermore, we derive rigorous error estimates for the fully discrete finite element scheme. Several numerical examples are presented to validate the accuracy, mass conservation and energy dissipation of the proposed scheme, and to illustrate complex biological phenomena, including the aggregation of multiple tumors of varying shapes and chemotaxis-driven growth patterns. The talk is based on two joint papers with Z Wang and J Yang, and with A Soenjaya and T Tran. |
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