UNCONDITIONALLY BOUND PRESERVING AND ENERGY DISSIPATIVE SCHEMES FOR A CLASS OF KELLER-SEGEL EQUATIONS

We propose numerical schemes for a class of Keller-Segel equations. The discretization is based on the gradient flow structure. The resulting first-order scheme is mass conservative, bound preserving, uniquely solvable, and energy dissipative, and the second-order scheme satisfies the first three properties. For parabolic-elliptic equations, the schemes are decoupled. Numerical examples are presented to show that besides the above properties, the schemes are efficient and able to capture the spiky solutions for the aggregation in chemotaxis.