  We propose a boundary value correction approach for cases when curved
boundaries are approximated by straight lines (planes) and Lagrange multipliers
are used to enforce Dirichlet boundary conditions. The approach allows for
optimal order convergence for polynomial order up to 3. We show the relation to
the Taylor series expansion approach used by Bramble, Dupont and Tom\'ee [Math.
Comp., 26:869--879, 1972] in the context of Nitsche's method and, in the case
of inf-sup stable multiplier methods, prove a priori error estimates with
explicit dependence on the meshsize and distance between the exact and
approximate boundary.
