$$
\newcommand{\dt}{\Delta t}
\newcommand{\tp}{\thinspace .}
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\x}{\boldsymbol{x}}
\renewcommand{\u}{\boldsymbol{u}}
\newcommand{\dx}{\, \mathrm{d}x}
\newcommand{\ds}{\, \mathrm{d}s}
\newcommand{\Real}{\mathbb{R}}
\newcommand{\ub}{u_{_\mathrm{D}}}
\newcommand{\GD}{\Gamma_{_\mathrm{D}}}
\newcommand{\GN}{\Gamma_{_\mathrm{N}}}
\newcommand{\GR}{\Gamma_{_\mathrm{R}}}
\newcommand{\inner}[2]{\langle #1, #2 \rangle}
\newcommand{\renni}[2]{\langle #2, #1 \rangle}
$$