In the 1980s three groups of jugglers came up with the same notation for juggling patterns. I'll explain this mathematical theory, demonstrating many examples, and show how it helps one understand the interplay of Gaussian elimination with column-rotation of matrices.
Abstract:
In this work we present a new mixed finite element method for a class of natural convection models describing the behavior of non-isothermal incompressible fluids subject to a heat source. More precisely, we consider a system based on the coupling of the steady-state equations of momentum (Navier-Stokes) and thermal energy by means of the Boussinesq approximation.
We propose and analyze a mixed formulation for the Brinkman-Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient, leading to a mixed formulation where the pseudostress tensor and the velocity are the main unknowns of the system. We establish existence and uniqueness of a solution to the weak formulation in a Banach space setting, employing classical results on nonlinear monotone operators and a regularization technique.
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