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!

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


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