Semi-discrete error estimates of the evolutionary Stokes equations with inhomogeneous Dirichlet boundary data

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Abstract

This work concerns finite element analysis of the evolutionary Stokes equation with inhomogeneous Dirichlet boundary data. The Dirichlet boundary data are enforced using a Lagrange multiplier approach generalized from the work of Gunzburger and Hou (1992) for the steady Stokes equations. With a practical choice of finite element spaces, the computation of the Lagrange multiplier–the boundary stress–is uncoupled from that of the velocity and the pressure. Various semi-discrete (in space) error estimates are presented for the velocity, pressure and the Lagrange multiplier.

Keywords

Evolutionary Stokes equations
Inhomogeneous Dirichlet boundary data
Error estimates
Finite element approximations
Lagrange multipliers

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