We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable from the system. It can be recovered by a simple post-processing. It is shown that the least-squares functional is uniformly equivalent, i.e., independent of the singular perturbation parameter, to a parameter dependent norm. This norm equivalence implies that the least-squares functional evaluated in the discrete solution provides an efficient and reliable a posteriori error estimator. Numerical experiments are presented.

翻译：我们定义并分析一种最小方位限制元素方法,用于对通过多孔介质流体流体流体的布林克曼模型进行一阶重整。 我们引入了一个假压力变量, 以便从系统中消除压力变量。 它可以通过简单的后处理回收。 显示最小方方位功能与参数依赖性规范一致, 即独立于单扰动参数。 这一规范等同意味着在离散解决方案中评估的最小方位功能提供了高效可靠的事后误差测算器。 演示了数值实验 。