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您的检索式：作者名="Mahboub Baccouch"
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| 1 | OPTIMAL A POSTERIORI ERROR ESTIMATES OF THE LOCAL DISCONTINUOUS GALERKIN METHOD FOR CONVECTION- DIFFUSION PROBLEMS IN ONE SPACE DIMENSION显示文摘在这份报纸,我们导出一个 posteriori 错误在一种空间尺寸为线性传送对流散开问题为本地不连续的 Galerkin (LDG ) 方法估计的最佳的顺序。在我们的分析的关键成分之一是最近的最佳的 superconvergence 结果在[杨·伊和 C.-W。Shu, J。Comp。数学, 33 (2015 ) , pp。323-340 ] 。我们首先证明分别地, LDG 答案和它的空间衍生物在 L2 标准收敛到(p + 1 ) 在网孔精炼下面的度权利和左 Radau 插入内推多项式。集中的顺序被证明是 p + 2,什么时候度的 piecewise 多项式至多, p 被使用。这些结果习惯于为溶液和它的衍生物的每个元素上的领先的错误术语与成正比的表演(p+1 ) 度权利和左 Radau 多项式。我们进一步证明那,为光滑的答案,估计,被作者在一份更早的报纸构造,集成的一个 posteriori LDG 错误在一确定的时间,评价到在在 O (hp+2 ) 的 L2 标准的真空间错误。最后,我们证明在 L2 标准的全球有效性索引以 O (h) 率收敛到统一。这些结果在我们在的以前出版的工作之上改善集中为的顺序估计和全球有效性索引的一个 posteriori 错误被证明分别地是 p+3/2 和 1/2。我们的证明为用有 p 的 Pp 多项式的任意的常规网孔是有效的 1。几个数字实验被执行验证理论结果。[从作者抽象] | Mahboub Baccouch | 2016 | Journal of Computational Mathematics2016，34，5： | 1 |
| 2 | Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second‑Order Elliptic Problems on Cartesian Grids显示文摘This paper is concerned with convergence and superconvergence properties of the local discontinuous Galerkin(LDG)method for two-dimensional semilinear second-order elliptic problems of the form−Δu=f(x,y,u)on Cartesian grids.By introducing special GaussRadau projections and using duality arguments,we obtain,under some suitable choice of numerical fuxes,the optimal convergence order in L2-norm of O(h^(p+1))for the LDG solution and its gradient,when tensor product polynomials of degree at most p and grid size h are used.Moreover,we prove that the LDG solutions are superconvergent with an order p+2 toward particular Gauss-Radau projections of the exact solutions.Finally,we show that the error between the gradient of the LDG solution and the gradient of a special Gauss-Radau projection of the exact solution achieves(p+1)-th order superconvergence.Some numerical experiments are performed to illustrate the theoretical results. | Mahboub Baccouch | 2022 | Communications on Applied Mathematics and Computation2022，4，2： | 0 |
| 3 | AN EFFICIENT FINITE DIFFERENCE METHOD FOR STOCHASTIC LINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS DRIVEN BY ADDITIVE WHITE NOISES显示文摘In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme. | Mahboub Baccouch | 2024 | Journal of Computational Mathematics2024，42，2： | 0 |
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