论文标题
固定的Boussinesq问题在单数强迫下
The stationary Boussinesq problem under singular forcing
论文作者
论文摘要
在Lipschitz的两个和三维结构域中，我们研究了在单数强迫下的热驱动对流模型的存在的存在。从单数来看，我们的意思是，允许热源属于$ h^{ - 1}（\ varpi，ω）$，其中$ \ varpi $是Muckenhoupt类$ a_2 $的重量，该$ a_2 $是在边界附近的常规的。我们提出了一个有限的元素方案，并在A_1 $中的$ \ varpi^{ - 1} \的假设下显示其收敛性。在热扩散和粘度是常数的情况下，我们提出了一个后验误差估计器，并显示其可靠性和局部效率。
In Lipschitz two and three dimensional domains, we study the existence for the so--called Boussinesq model of thermally driven convection under singular forcing. By singular we mean that the heat source is allowed to belong to $H^{-1}(\varpi,Ω)$, where $\varpi$ is a weight in the Muckenhoupt class $A_2$ that is regular near the boundary. We propose a finite element scheme and, under the assumption that the domain is convex and $\varpi^{-1} \in A_1$, show its convergence. In the case that the thermal diffusion and viscosity are constants, we propose an a posteriori error estimator and show its reliability and local efficiency.
