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您的检索式：作者名="Alexandre Ern"
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| 1 | A POSTERIORI ENERGY-NORM ERROR ESTIMATES FOR ADVECTION-DIFFUSION EQUATIONS APPROXIMATED BY WEIGHTED INTERIOR PENALTY METHODS显示文摘我们建议错误与异构、各向异性的散开为加权的内部惩罚估计 advection-diffusion-reaction 方程的不连续的 Galerkin 近似并且分析后验精力标准。重量,在分析起一个关键作用,取决于散开张肌并且被用来在不连续的 Galerkin 方法提出一致性术语。错误上面的界限,所有常数在被指定,由三个术语组成:仅仅取决于元素的一个剩余评估者分离溶液剩余,在方法使用的重量明确地进入的一个散开的流动评估者,和是因为不连续的有限元素空格的使用的非零的一个非遵守的评估者的明智的变化。三个评估者能被近似错误局部地围住。注意在本地人在常数的问题参数上被给相关性的详细规格降低错误界限。为中等移流,关于散开异质的完整的坚韧性在不连续的 Galerkin 方法由于重量的特定的设计被完成,这被显示出,当时完全本地的散开 anisotropies 遗体和影响通过条件的方形的根的常数散开张肌数。为主导的移流,它被显示出,在由连续有限元素上的 Verf ür th 的以前的工作的精神,本地人降低错误界限,这能被写,常数包含一为本地网孔尺寸到的比率截止散开张肌的最低本地 eignevalue 的方形的根相互。 | Alexandre Ern AnnetteF.Stephansen | 2008 | Journal of Computational Mathematics2008，26，4： | 2 |
| 2 | Hybrid High‑Order Methods for the Acoustic Wave Equation in the Time Domain显示文摘We devise hybrid high-order(HHO)methods for the acoustic wave equation in the time domain.We frst consider the second-order formulation in time.Using the Newmark scheme for the temporal discretization,we show that the resulting HHO-Newmark scheme is energy-conservative,and this scheme is also amenable to static condensation at each time step.We then consider the formulation of the acoustic wave equation as a frst-order system together with singly-diagonally implicit and explicit Runge-Kutta(SDIRK and ERK)schemes.HHO-SDIRK schemes are amenable to static condensation at each time step.For HHO-ERK schemes,the use of the mixed-order formulation,where the polynomial degree of the cell unknowns is one order higher than that of the face unknowns,is key to beneft from the explicit structure of the scheme.Numerical results on test cases with analytical solutions show that the methods can deliver optimal convergence rates for smooth solutions of order O(hk+1)in the H1-norm and of order O(h^(k+2))in the L^(2)-norm.Moreover,test cases on wave propagation in heterogeneous media indicate the benefts of using high-order methods. | Erik Burman Omar Duran Alexandre Ern | 2022 | Communications on Applied Mathematics and Computation2022，4，2： | 0 |
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