Polynomial robust stability analysis for $H(\textrm{div})$-conforming finite elements for the Stokes equations

摘要: In this work we consider a discontinuous Galerkin method for the discretization of Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such exact mass conservation and pressure-independent error estimates. The main aspect lies in analysis high order approximations. show that considered is uniformly stable with respect to polynomial $k$ provides optimal estimates $ \| \boldsymbol{u} - \boldsymbol{u}_h \|_{1_h} + \Pi^{Q_h}p-p_h \le c \left( h/k \right)^s \|_{s+1} $. To derive those estimates, prove $k$-robust LBB condition. This proof based on $H^2$-stable extension operator. operator itself interest numerical $C^0$-continuous methods $4^{th}$ problems.