论文标题
Darcy-Forchheimer问题的数值离散和奇异热方程
Numerical discretization of a Darcy-Forchheimer problem coupled with a singular heat equation
论文作者
论文摘要
在Lipschitz结构域中，我们研究了Darcy-Forchheimer问题，并根据温度取决于非线性强迫术语，并通过非线性强迫术语进行奇异的热方程。通过单数，我们的意思是热源对应于狄拉克度量。我们为模型建立了解决方案的存在，该模型可以根据温度在热方程中扩散系数。对于这样的模型，我们还提出了有限的元素离散化方案，并提供了先验收敛分析。在上述扩散系数是恒定的情况下，我们设计了一个后验误差估计器并调查可靠性和效率属性。我们通过根据提出的误差估计器设计自适应循环并提出数值实验来结束。
In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish the existence of solutions for a model that allows a diffusion coefficient in the heat equation depending on the temperature. For such a model, we also propose a finite element discretization scheme and provide an a priori convergence analysis. In the case that the aforementioned diffusion coefficient is constant, we devise an a posteriori error estimator and investigate reliability and efficiency properties. We conclude by devising an adaptive loop based on the proposed error estimator and presenting numerical experiments.
