# P1 Finite element discretisation of laplace-neumann eigenproblem

I am looking for help in the FE discretisation of the Laplace eigenkproblem with Neumann boundary conditions; that is, $$-\int_{\Omega} \nabla u \cdot \nabla v= \lambda \int_{\Omega} uv,$$ or $$Ax=\lambda_j Mx,$$ where $$A$$,$$M$$ are the stiffness and mass matrices, respectively. If it's easier, I would like to assemble $$M$$ with mass lumping. I have my own triangulation with sets of vertices, coordinates, triangles, etc. I understand how to assemble $$A$$ (computed the nodal areas, connectivity, etc), but any help with $$M$$ would be very appreciated. From my understanding, with the mass lumping, $$M$$ will be diagonal, but I'm not sure how it would vary from the identity matrix. I suppose my main question is how to assemble a finite element mass matrix in 2D with P1 finite elements!

• What have you tried already? You might want to write down the definition of $M$, and then say how you want to compute integrals. Jan 10 at 13:06