3 papers
math.NA2025
-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.NA2025
Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization
Xiaobing Feng, Liet Vo
This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of…
math.NA2025
Optimal Order Space-Time Discretization Methods for the Nonlinear Stochastic Elastic Wave Equations with Multiplicative Noise
Xiaobing Feng, Yukun Li, Liet Vo
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with mult…