论文标题
达西的问题以及在单数强迫下的热方程式：分析和离散化
Darcy's problem coupled with the heat equation under singular forcing: analysis and discretization
论文作者
论文摘要
我们研究了达西问题的解决方案以及在单数强迫下的热方程式的存在。热方程的右侧对应于狄拉克度量。研究的模型可以根据温度而进行热扩散和粘度。我们提出了有限元溶液技术并分析其收敛性。在热扩散是恒定的情况下，我们提出了一个后验误差估计器并调查可靠性和效率属性。我们用数值示例说明了理论。
We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity depending on the temperature. We propose a finite element solution technique and analyze its convergence properties. In the case that the thermal diffusion is constant, we propose an a posteriori error estimator and investigate reliability and efficiency properties. We illustrate the theory with numerical examples.
