2016/07/26 by Guosheng Fu, Fu, Guosheng, Yanyi Jin +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Discontinuous Galerkin method #FOS: Mathematics #Finite element method #Flow (mathematics) #Geometry #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Physics #Polygon mesh #Stokes flow #Superconvergence
paper · pdf · doi:10.48550/arxiv.1607.07662
openalex publication_date 2016/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we present new parameter-free superconvergent H(div)-conforming HDG methods for the Brinkman equations on both simplicial and rectangular meshes. The methods are based on a velocity gradient-velocity-pressure formulation, which can be considered as a natural extension of the H(div)-conforming HDG method (defined on simplicial meshes) for the Stokes flow [Math. Comp. 83(2014), pp. 1571-1598]. We obtain optimal error estimates in L2-norms for all the variables in both the Stokes-dominated regime (high viscosity/permeability ratio) and Darcy-dominated regime (low viscosity/permeability ratio). We also obtain superconvergent L2-estimate of one order higher for a suitable projection of the velocity error, which is typical for (hybrid) mixed methods for elliptic problems. Moreover, thanks to H(div)-conformity of the velocity, our velocity error estimates are independent of the pressure regularity. Preliminary numerical results on both triangular and rectangular meshes in two-space dimensions confirm our theoretical predictions.