Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis (Q706230)

The authors study the influence of approximation errors in the Dirichlet boundary data for finite element approximations of elliptic partial differential equations. Quantitative a priori and a posteriori estimates are presented for the nodal interpolation and the \( L^2 \) orthogonal projections. It is observed that the \( L^2 \) projetion of the given Dirichlet data onto the trace space of the finite element functions on the boundary gives always higher order contributions in posteriori estimates than the nodal interpolation (cf. \textit{C. Carstensen} and \textit{S. Bartels} [Math. Comp. 71, 945--969 (2002; Zbl 0997.65126)]).