论文标题
Darcy-Forchheimer问题的后验错误估计与对流扩散反应方程相结合
A Posteriori error estimates for Darcy-Forchheimer's problem coupled with the convection-diffusion-reaction equation
论文作者
论文摘要
在这项工作中，我们通过非线性外部来源得出对流 - 扩散反应方程以及Darcy-Forchheimer问题的后验错误估计，具体取决于流体的浓度。我们介绍了与问题相关的变异公式，并通过使用有限元方法将其离散。我们证明了具有两种类型的可计算误差指标的后验错误。第一个链接到线性化，第二个链接到离散化。然后，我们在精确解决方案的其他规律性假设下发现上下错误界限。最后，进行数值计算以显示获得的误差指标的有效性。
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the variational formulation associated to the problem, and discretize it by using the finite element method. We prove optimal a posteriori errors with two types of calculable error indicators. The first one is linked to the linearization and the second one to the discretization. Then we find upper and lower error bounds under additional regularity assumptions on the exact solutions. Finally, numerical computations are performed to show the effectiveness of the obtained error indicators.
