I'm searching for lower bounds of bilinear forms arising in FEM for elliptic second order PDEs with mixed boundaries.
I did some research and found:
$$\max_{v_{h}\in\mathcal{V}_h(\mathcal{\Omega})}a(v_{h}, v_{h}) \geq Ch^{d-2}\, ,$$
where $d$ is the Dimension of the domain, $C$ a positive constant and $h$ the mesh size.
The bilinear form is defined as $a(v_h,v_h):= \int_\Omega \nabla v_h A \nabla v_h \, d\Omega$ and $A$ is an elliptic operator.
I found this bound quite often but not a single proof to it. Does anyone know some literature or how the proof works?