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A mixed discontinuous Galerkin method for an unsteady incompressible Darcy equation
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-06-05 , DOI: 10.1080/00036811.2020.1775818
Yanxia Qian 1 , Fei Wang 2 , Yongchao Zhang 1 , Weimin Han 3
Affiliation  

We study a mixed discontinuous Galerkin (MDG) method for solving a time-dependent Darcy problem, which simulates an incompressible fluid such as water flowing in a rigid porous medium. The discretization of the unsteady Darcy problem relies on a backward Euler scheme for temporal variable and MDG method for spatial variables. Spatially semi-discrete and fully discrete schemes are analyzed. Existence and uniqueness of the numerical solutions are proved, and optimal order error estimates are derived for both the velocity and pressure variables. Finally, some test problems are provided to display the performance of the MDG method, and numerical results are reported to support the theoretical predictions.



中文翻译:

非定常不可压缩达西方程的混合间断伽辽金法

我们研究了一种混合不连续伽辽金 (MDG) 方法来解决时间相关的达西问题,该方法模拟不可压缩的流体,例如在刚性多孔介质中流动的水。非定常达西问题的离散化依赖于时间变量的后向欧拉方案和空间变量的MDG方法。分析了空间半离散和全离散方案。证明了数值解的存在性和唯一性,导出了速度和压力变量的最优阶误差估计。最后,提供了一些测试问题来展示 MDG 方法的性能,并报告了数值结果以支持理论预测。

更新日期:2020-06-05
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