论文标题
一阶系统最小二乘有限元法，用于奇异的darcy方程
First-order system least-squares finite element method for singularly perturbed Darcy equations
论文作者
论文摘要
我们定义和分析了最小二乘有限元方法，以通过多孔培养基的流体流量的缩放型布林克曼模型进行一阶重新印象。我们引入了一个伪色变量，该变量允许从系统中消除压力变量。可以通过简单的后处理来恢复它。结果表明，最小二乘函数在统一的扰动参数上均匀等效，即独立于参数依赖性标准。该规范等效性意味着在离散解决方案中评估的最小二乘功能提供了有效且可靠的后验误差估计器。提出了数值实验。
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.
