论文标题
有限元素appoximation和增强的拉格朗日预处理，用于含有含量的非纽顿流动
Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow
论文作者
论文摘要
我们设计了一个系统的3场和四场有限元近似值，该系统描述了具有隐式非牛顿流变学的不可压缩热传导流体的稳态。我们证明，数值近似的序列会收敛到问题的弱解。我们基于增强的拉格朗日稳定化开发一个块预处理，以基于Scott-Vogelius有限元对的离散化，以实现速度和压力。预处理涉及一种专门的多式算法，该算法利用了捕获散发和非标准的间接传输操作员内核的空间分类。当应用于Navier-Stokes和幂律系统（包括温度依赖性粘度，热电导率和粘性耗散）时，预处理器表现出强大的收敛行为。
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations converges to a weak solution of the problem. We develop a block preconditioner based on augmented Lagrangian stabilisation for a discretisation based on the Scott-Vogelius finite element pair for the velocity and pressure. The preconditioner involves a specialised multigrid algorithm that makes use of a space-decomposition that captures the kernel of the divergence and non-standard intergrid transfer operators. The preconditioner exhibits robust convergence behaviour when applied to the Navier-Stokes and power-law systems, including temperature-dependent viscosity, heat conductivity and viscous dissipation.
