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Projection-Based Structure-Preserving Scheme for Patlak-Keller-Segel Equations on Surfaces
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DOI：10.1002/num.70087.png)
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Abstract
En 中文
In this article, we propose and analyze an efficient projection-based structure-preserving scheme for Patlak-Keller-Segel equations on surfaces. The mass lumping surface finite element method is adopted for the spatial discretization. The time integration is based on the second-order Crank-Nicolson/Adams-Bashforth scheme via an L-2 projection post-processing strategy and scalar auxiliary variable approach, which is proven to be bound/positivity preserving, mass conservative, and energy stable with the modified energy. Rigorous convergence analysis is presented, achieving an optimal spatial convergence rate. Various numerical examples are performed to verify these theoretical results and demonstrate the efficiency and robustness of the proposed scheme.
Keywords:
energy stability
mass conservation
mass lumping surface finite element method
Patlak-Keller-Segel equations on surfaces
unconditional bound/positivity preservation
Journal
N
IF:
1.7
Papers:
46
Citations:
3.9K