Hello everyone,
consider I have a F\in\mathbb{R}^{3\times 2} Flux matrix and a testfunction \varphi\in\mathbb{R}^{3} on a triangle element \Omega in 2D. I want to rewrite \int_{\partial\Omega}F\cdot\varphi\cdot n dS, which occurs during the use of the DG method. I already know that I have to rewrite it in terms of integral over edges but i dont know how. Normally i would approximate the boundary integral with a numerical flux. How is this handled in fenics?
Fyi: F=\begin{pmatrix}-C_1+1 & -C_2+1\\-\frac{1}{\lambda}u & 0\\0&-\frac{1}{\lambda}u\end{pmatrix} where C1, C2 and u are the variables and \lambda is a constant.
Thank you in advance for your help!