2022
DOI: 10.3934/cpaa.2021074
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Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations

Abstract: In this paper, we investigate fully discrete schemes for the Allen-Cahn and Cahn-Hilliard equations respectively, which consist of the stabilized finite element method based on multiscale enrichment for the spatial discretization and the semi-implicit scheme for the temporal discretization. With reasonable stability conditions, it is shown that the proposed schemes are energy stable. Furthermore, by defining a new projection operator, we deduce the optimal L 2 error estimates. Some numerical experiments are pr… Show more

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“…The step function is the focus of local path planning strategy implementation based on deep reinforcement learning, which involves two key issues:one is how to describe the observable state space, and the other is how to design the reward function [10] . The former reflects the environmental information that the observer needs to pay attention to during the implementation of local path planning, and the latter can guide the local path planning strategy to update in the direction of the goal [11] .…”
Section: Observable State and Reward Function Designmentioning
confidence: 99%
“…The step function is the focus of local path planning strategy implementation based on deep reinforcement learning, which involves two key issues:one is how to describe the observable state space, and the other is how to design the reward function [10] . The former reflects the environmental information that the observer needs to pay attention to during the implementation of local path planning, and the latter can guide the local path planning strategy to update in the direction of the goal [11] .…”
Section: Observable State and Reward Function Designmentioning
confidence: 99%