  We present and analyze a weak Galerkin finite element method for solving the
transport-reaction equation in $d$ space dimensions. This method is highly
flexible by allowing the use of discontinuous finite element on general meshes
consisting of arbitrary polygon/polyhedra. We derive the
\textcolor[rgb]{0.00,0.00,1.00}{$L_2$-error estimate} of
$O(h^{k+\frac{1}{2}})$-order for the discrete solution when the $k$th-order
polynomials are used for $k\geq 0$. Moreover, for a special class of meshes, we
also obtain the \textcolor[rgb]{0.00,0.00,1.00}{optimal error} estimate of
$O(h^{k+1})$-order in the $L_2$-norm. A derivative recovery formula is
presented to approximate the convection
\textcolor[rgb]{1.00,0.00,0.00}{directional derivative} and the corresponding
superconvergence estimate is given. Numerical examples on compatible and
non-compatible meshes are provided to show the effectiveness of this weak
Galerkin method.
