Conforming finite element space
= Conforming finite element space
{title2=$V_h\subseteq V$}
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>.