Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 491, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2023.112346
Keywords
High order computation; Optimal transport; Mean-field planning; Mean-field games
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This work explores the application of general high-order numerical schemes with finite element methods in the space-time domain for computing optimal transport, mean-field planning, and potential MFG problems. Several experiments are conducted to validate the convergence rate of the high-order method numerically, demonstrating the efficiency and effectiveness of the approach.
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In this work, we explore applying general high-order numerical schemes with finite element methods in the space-time domain for computing the optimal transport (OT), mean-field planning (MFP), and potential MFG problems. We conduct several experiments to validate the convergence rate of the high order method numerically. Those numerical experiments also demonstrate the efficiency and effectiveness of our approach. (c) 2023 Elsevier Inc. All rights reserved.
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