Fundamental Areas / Numerical Analysis of Partial Differential Equations
This video illustrates the adaptive algorithm of a pseudostress-based mixed finite element method for the two-dimensional nonlinear Brinkman model of porous media flow with mixed boundary conditions. The main unknowns are a tensor field σ (pseudostress), a vector field u (velocity), and a scalar field p (pressure) in appropriate spaces. The example above considers a T-shaped domain with singularities around the corners (-0.25,0.5) and (0.25, 0.5), and along the line x2 = -1. Further details are available in the paper:
Gatica, G.N., Gatica, L.F. and Sequeira, F.: Analysis of an augmented pseudostress-based mixed formulation for a nonlinear Brinkman model of porous media flow. Computer Methods in Applied Mechanics and Engineering, vol. 289, 1, pp. 104-130, (2015).