Consider the following two point BVP:$$-u''(x)=f(x),~~~u(0)=u(1)=0.$$An interior penalty DG method for this BVP that weakly imposes homogeneous Dirichlet boundary conditions is of the form:$$\sum_{i=0}^{N-1} \int_{I_i} u'(x) v'(x)\,dx+\frac{1}{h}\sum_{i=0}^{N } [\![u]\!]|_{x_i}  [\![ v]\!]|_{x_i} - \epsilon (\!( v')\!)|_{x_i}      [\![ u ]\!]|_{x_i}   - (\!( u')\!)|_{x_i}      [\![ v ]\!]|_{x_i}  =\int_{0}^{1} f(x)v(x)\,dx,$$where $[\![ \cdot ]\!]$ is the jump operator, and $(\!( \cdot )\!)$ is the average operator (see for more detail: https://scicomp.stackexchange.com/questions/19394/help-implementing-1d-ode-discontinuous-galerkin-method).Question:  How can I modify the above interior penalty DG method so that it can handle Neumann boundary conditions?  For Poisson's equation in 2D and 3D, I've seen Neumann boundary conditions handled through integrals on the boundary of the elements...not sure if there is analogy of this for ODEs...
How to impose Neumann boundary conditions in interior penalty DG method
pde;discontinuous galerkin;elliptic pde