Computing corresponding values of the Neumann and Dirichlet boundary values for incompressible Stokes flow (Q618731)

The numerical analysis of the unsteady 2D Stokes problem is the subject of the paper. The velocity vector \(v(x,t)\) and the pressure \(p(x,t)\) satisfy the equations \[ \frac{\partial v}{\partial t}-\nu\nabla\cdot(\nabla v+(\nabla v)^T)+\nabla p=f,\quad \operatorname{div}v=0, \] where \(x\) belongs to a connected compact set \(\Omega\subset{\mathbb R}^2\), \(t\in[0,T]\). The problem is investigated by the Galerkin FEM. The authors are interested in the relationship of the values of the velocity field at the inflow edge (Dirichlet boundary values) and the values for the force at the edge (Neumann boundary values). This relationship is determined first for the steady state case and then for the nonsteady case. An interesting example is considered in the paper.