Numerical computations with H(div)-finite elements for the Brinkman problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in Konno and Stenberg (2010; Math Models Methods Appl Sci, 2011). Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.