A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem (Q5959270)

The authors consider the following nonhomogeneous Dirichlet problem \[ \begin{cases} -\Delta u=f\quad &\text{in }\Omega,\\ u= q\quad &\text{on }\Gamma,\end{cases} \] where \(\Omega\) is a planar polygonal domain and \(\Gamma\) its frontier. The solution of this problem is approximated by an affine finite element method (FEM) scheme on a triangular mesh. The purpose of the paper is to study howe errors in the approximation of \(q\) influence the FEM approximation and to give a posteriori error estimates. Numerical examples illustrate the difficulties arising in such estimates, and that the proposed estimators are reliable.