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Superconvergence of Numerical Gradient for Weak Galerkin Finite Element Methods on Nonuniform Cartesian Partitions in Three Dimensions

Li, Dan; Nie, Yufeng; Wang, Chunmei (January 2019, Computers mathematics with applications)

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Superconvergence of Numerical Gradient for Weak Galerkin Finite Element Methods on Nonuniform Cartesian Partitions in Three Dimensions

Li, Dan; Nie, Yufeng; Wang, Chunmei (January 2019, Computers mathematics with applications)
null (Ed.)
Full Text Available
Superconvergence of Numerical Gradient for Weak Galerkin Finite Element Methods on Nonuniform Cartesian Partitions in Three Dimensions

Li, Dan; Nie, Yufeng; Wang, Chunmei (January 2019, Computers & mathematics with applications)

Full Text Available
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system

https://doi.org/10.1002/num.22829

Gao, Yali; He, Xiaoming; Nie, Yufeng (August 2021, Numerical Methods for Partial Differential Equations)

Abstract In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.
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