Finite Element Method Inverse Estimate - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T13:01:43Z http://mathoverflow.net/feeds/question/56400 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56400/finite-element-method-inverse-estimate Finite Element Method Inverse Estimate alext87 2011-02-23T14:41:37Z 2011-02-23T15:16:11Z <p>Looking for a proof in the literature of the following lemma:</p> <p>Let $K\subset\mathbb{R}^d$ be a bounded domain. Let $P_X$ be a finite dimensional subspace of $\mathcal{H}^k(K)$ then</p> <p><code>$$\left\|v\right\|_{\mathcal{H}^k(K)} \leq C diam(K)^{-k} \left\|v\right\|_{L_2(K)}$$</code></p> <p>for all $v\in P_X$ and where the constant $C$ does not depend on $diam(K)$. </p> <p>There is a proof in The mathematical theory of finite element method By Susanne C. Brenner, L. Ridgway Scott p111 but they do not check if the constant $C$ is independent of $diam(K)$.</p> <p>Thanks in advance.</p>