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Volume 43, Issue 5
An Oscillation-Free Discontinuous Galerkin Method for a Nonlinear Stochastic Convection-Dominated Diffusion Problem and Its Error Analysis

Yaping Li, Weidong Zhao & Wenju Zhao

DOI: 10.4208/jcm.2407-m2023-0265

J. Comp. Math., 43 (2025), pp. 1264-1289.

Published online: 2025-09

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  • Abstract

In this paper, an effective oscillation-free discontinuous Galerkin (DG) scheme for a nonlinear stochastic convection-dominated problem is formulated and analyzed. The proposed oscillation-free scheme is capable to capture the steep fronts of solution automatically and distinguish the influence of the convection domination and noise perturbation. Under proper regularity assumptions, the optimal convergence rates in space and time are rigorously proved with the techniques of variational solution and conditional expectation. In the numerical simulation, the classical SIPG scheme and the proposed oscillation-free DG scheme are both performed and compared. The numerical convergence rates tests are first carried out to verify the theoretical results. The benchmark tests having the steep behaviors are further provided to illustrate the effectiveness and robustness of our proposed oscillation-free DG scheme.

  • Keywords

Stochastic convection-domination, Discontinuous Galerkin method, Conditional expectation technique, Euler-Maruyama approach, Error estimates.

  • AMS Subject Headings

60H15, 65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-1264, author = {Li , YapingZhao , Weidong and Zhao , Wenju}, title = {An Oscillation-Free Discontinuous Galerkin Method for a Nonlinear Stochastic Convection-Dominated Diffusion Problem and Its Error Analysis}, journal = {Journal of Computational Mathematics}, year = {2025}, volume = {43}, number = {5}, pages = {1264--1289}, abstract = {

In this paper, an effective oscillation-free discontinuous Galerkin (DG) scheme for a nonlinear stochastic convection-dominated problem is formulated and analyzed. The proposed oscillation-free scheme is capable to capture the steep fronts of solution automatically and distinguish the influence of the convection domination and noise perturbation. Under proper regularity assumptions, the optimal convergence rates in space and time are rigorously proved with the techniques of variational solution and conditional expectation. In the numerical simulation, the classical SIPG scheme and the proposed oscillation-free DG scheme are both performed and compared. The numerical convergence rates tests are first carried out to verify the theoretical results. The benchmark tests having the steep behaviors are further provided to illustrate the effectiveness and robustness of our proposed oscillation-free DG scheme.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2407-m2023-0265}, url = {http://global-sci.org/intro/article_detail/jcm/24481.html} }
TY - JOUR T1 - An Oscillation-Free Discontinuous Galerkin Method for a Nonlinear Stochastic Convection-Dominated Diffusion Problem and Its Error Analysis AU - Li , Yaping AU - Zhao , Weidong AU - Zhao , Wenju JO - Journal of Computational Mathematics VL - 5 SP - 1264 EP - 1289 PY - 2025 DA - 2025/09 SN - 43 DO - http://doi.org/10.4208/jcm.2407-m2023-0265 UR - https://global-sci.org/intro/article_detail/jcm/24481.html KW - Stochastic convection-domination, Discontinuous Galerkin method, Conditional expectation technique, Euler-Maruyama approach, Error estimates. AB -

In this paper, an effective oscillation-free discontinuous Galerkin (DG) scheme for a nonlinear stochastic convection-dominated problem is formulated and analyzed. The proposed oscillation-free scheme is capable to capture the steep fronts of solution automatically and distinguish the influence of the convection domination and noise perturbation. Under proper regularity assumptions, the optimal convergence rates in space and time are rigorously proved with the techniques of variational solution and conditional expectation. In the numerical simulation, the classical SIPG scheme and the proposed oscillation-free DG scheme are both performed and compared. The numerical convergence rates tests are first carried out to verify the theoretical results. The benchmark tests having the steep behaviors are further provided to illustrate the effectiveness and robustness of our proposed oscillation-free DG scheme.

Li , YapingZhao , Weidong and Zhao , Wenju. (2025). An Oscillation-Free Discontinuous Galerkin Method for a Nonlinear Stochastic Convection-Dominated Diffusion Problem and Its Error Analysis. Journal of Computational Mathematics. 43 (5). 1264-1289. doi:10.4208/jcm.2407-m2023-0265
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