Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation

Abstract

This work concerns the analysis and finite element approximations of the evolutionary Stokes equations, with inhomogeneous boundary and divergence data. The proposed weak formulation can be viewed as an attempt to develop the parabolic analog of the well known saddle point theory for elliptic problems. Several results concerning the analysis and finite element approximations are presented. The key feature of the weak formulation under consideration is the treatment of Dirichlet boundary conditions within the Lagrange multiplier framework.