Thank you. I understand. But I think it can be interesting to test coercivity by numerical investigation.
Suppose one have DG method for problem and theory is not known or not known to engineer.
Testing convergence is very good, then engineer can know method is ok. It will guarantee good method in range of h tested.
Test of coercivity, maybe can complement test convergence. Idea: Compute approximate constant in A(v,v) >= C||v||. If C very large, engineer is safe. If C small, then need more investigation such as convergence investigation.
Expensive investigation for finding C is maybe ok. Must be compared with cost of mesh refine and testing convergence, if this can be avoided.
Perhaps eigenvalue problem of A? Minimum eigenvalue?
Thank you for reading!