Let $V$ be a real [Hilbert space](/page/Hilbert%20Space) with norm $\|\cdot\|_V$, let $a:V\times V\to\mathbb R$ be a [bilinear form](/page/Bilinear%20Form), and let $F:V\to\mathbb R$ be a bounded linear functional. Assume that $a$ is continuous and coercive: there are constants $M,\alpha>0$ such that $|a(u,v)|\le M\|u\|_V\|v\|_V$ and $a(v,v)\ge \alpha\|v\|_V^2$ for all $u,v\in V$. If $V_h$ is a linear subspace of $V$, and if $u\in V$ and $u_h\in V_h$ solve $a(u,v)=F(v)$ for all $v\in V$ and $a(u_h,v_h)=F(v_h)$ for all $v_h\in V_h$, then

\begin{align*} \|u-u_h\|_V\le \frac{M}{\alpha}\inf_{v_h\in V_h}\|u-v_h\|_V. \end{align*}