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Structure Preserving Schemes for Fokker–Planck Equations of Irreversible Processes

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Abstract

In this paper, we construct structure preserving schemes for solving Fokker–Planck equations associated with irreversible processes. The proposed method is first order in time. We consider two structure-preserving spatial discretizations, which are second order and fourth order accurate finite difference schemes. They are derived via finite difference implementation of the classical \(Q^k\) (\(k=1,2\)) finite element methods on uniform meshes. Under mild mesh conditions and practical time step constraints, the schemes are proved monotone, thus are positivity-preserving and energy dissipative. In particular, our scheme is suitable for capturing steady state solutions in large final time simulations.

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Funding

Yuan Gao’s research was supported by NSF Grant DMS-2204288. Xiangxiong Zhang’s research was supported by NSF Grant DMS-1913120.

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Yuan Gao’s research was supported by NSF Grant DMS-2204288. Xiangxiong Zhang’s research was supported by NSF Grant DMS-1913120.

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Liu, C., Gao, Y. & Zhang, X. Structure Preserving Schemes for Fokker–Planck Equations of Irreversible Processes. J Sci Comput 98, 4 (2024). https://doi.org/10.1007/s10915-023-02378-0

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