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math.NA2024
-convergence of an Enhanced Finite Element Method for Manià's and Foss's Problems Exhibiting the Lavrentiev Gap Phenomenon
Xiaobing Feng, Joshua M. Siktar
It is well-known that numerically approximating calculus of variations problems possessing a Lavrentiev Gap Phenomenon (LGP) is challenging, and the standard numerical methodologie…
math.NA2024
Optimal order time discretizations for stochastic semilinear wave equations with multiplicative noise
Xiaobing Feng, Yukun Li, Liet Vo
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The…
math.NA2024
Mathematical and numerical analysis for PDE systems modeling intravascular drug release from arterial stents and transport in arterial tissue
Xiaobing Feng, Tingao Jiang
This paper is concerned with the PDE and numerical analysis of a modified one-dimensional intravascular stent model originally proposed in [4]. It is proved that the modified model…