Let $M$ be a triangulated domain with the functionspace: \[W_{PL}:=\bigl\{f:M\rightarrow\mathbb{R}\,\bigl\vert\bigr.\,\,\,\left. f\right|_{T_{\sigma}} \mbox{ is affine for all } \sigma \in \Sigma_2 \bigr\}.\] On the interior of each triangle $T_{\sigma}$ in $M$ the gradient of a function $g \in W$ is well … Continue reading Gradient and Dirichlet energy on triangulated domains.