I am working on a method based on moving least square approximation where shape functions  do not satisfy Kroneker Delta property. So Dirichlet boundary condition should be enforced.I usually used penalty method for that. In the error estimation based on residual I used the following for Poisson equation:\begin{align}\eta^2=h_T^2\Vert  \Delta u+f \Vert^2+h_T^{-1} \Vert u-g_D\Vert^2_{\partial \Omega}.\end{align} where\begin{align}-\Delta u=f, \quad u_{|\partial \Omega}=g_D.\end{align}Also, it should be noted that, because of the shape functions there is no jump between the internal elements.The problem is that penalty parameter $\gamma$ should be bigger than $1e3$ to get good result. But for large $\gamma$ the effect of adaptive technique is not really good. All the time results by adaptive refinement is better than uniform. But when $\gamma$ is smaller for example $\gamma< 1e2$ the difference is remarkable. By these results I guess the term relates to Dirichlet boundary should be change by $\gamma$. But how? 
Dirichlet term in error estimations
finite element;error estimation;meshless methods
It is quite well known in finite element research community that penalty methods easily lead to under/over refinement when used with adaptive methods, see for example the numerical examples in the end of Juntunen, Stenberg: Nitsche's method for general boundary conditions (page 1373). If you want to enforce the boundary conditions weakly, I would advise you to use Nitsche's method instead.