An Oscillation-Free Discontinuous Galerkin Method for a Nonlinear Stochastic Convection-Dominated Diffusion Problem and Its Error Analysis (Journal of Computational Mathematics, 2025)
In this paper, an effective oscillation-free discontinuous Galerkin (DG) scheme for a nonlinear stochastic convection-dominated problem is formulated and analyzed. The proposedoscillation-free scheme is capable to capture the steep fronts of solution automatically anddistinguish the influence of the convection domination and noise perturbation. Underproper regularity assumptions, the optimal convergence rates in space and time are rigorously proved with the techniques of variational solution and conditional expectation. Inthe numerical simulation, the classical SIPG scheme and the proposed oscillation-free DGscheme are both performed and compared. The numerical convergence rates tests are firstcarried out to verify the theoretical results. The benchmark tests having the steep behaviors are further provided to illustrate the effectiveness and robustness of our proposedoscillation-free DG scheme.
Keywords: Stochastic convection-domination; Discontinuous Galerkin method; Conditional expectation technique; Euler-Maruyama approach; Error estimates.