Conforming finite element space ($V_h\subseteq V$)

A conforming finite element space is a finite-dimensional vector subspace of the solution's variational space $V$. For a second-order problem with homogeneous Dirichlet boundary conditions, continuous piecewise-polynomial functions vanishing on the boundary form such a subspace of the zero-boundary Sobolev space $H_0^1(\Omega )$. Conformity allows exact Galerkin orthogonality and the Céa lemma.