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math.NA2025
High-order mass conserving, positivity plus energy-law preserving schemes and their error estimates for Keller-Segel equations
Mingmei Chen, Kun Wang, Cong Xie
Chemotaxis plays a significant role in numerous physiological processes. The Keller-Segel equation serves as a mathematical model for simulating the phenomenon of cell population a…
math.NA2022
On a novel numerical quadrature based on cycle index of symmetric group for the Hadamard finite-part integrals
Jiajie Yao, Congcong Xie
To evaluate the Hadamard finite-part integrals accurately, a novel interpolatory-type quadrature is proposed in this article. In our approach, numerical divided difference is utili…
math.NA2018
Superconvergent Gradient Recovery for Virtual Element Methods
Hailong Guo, Cong Xie, Ren Zhao
Virtual element methods is a new promising finite element methods using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In th…