Rodolfo Araya, Manuel Solano, Patrick Vega:
Analysis of an adaptive HDG method for the Brinkman problem
We introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for the gradient-velocity-pressure formulation of the Brinkman problem. We present an a priori error analysis of the method, showing optimal order of convergence of the error. We also introduce an a posteriori error estimator, of the residual type, which helps us to improve the quality of the numerical solution. We establish reliability and local eciency of our estimator for the L2-error of the velocity gradient and the pressure and the H1-error of the velocity, with constants which are independent of the physical parameters and the size of the mesh. In particular, our results are also valid for the Stokes problem. Finally, we provide numerical experiments showing the quality of our adaptive scheme.
This preprint gave rise to the following definitive publication(s):
Rodolfo ARAYA, Manuel SOLANO, Patrick VEGA: Analysis of an adaptive HDG method for the Brinkman problem. IMA Journal of Numerical Analysis, vol. 39, 3, pp. 1502-1528, (2019).