Consider the problem $-\Delta u = f$ in $\Omega$, with $u=0$ on $\partial \Omega$. Suppose that $\Omega$ is a polygon and that we approximate the solutions to the previous problem using Lagrange finite elements on a triangular mesh. When solving such a finite element problem there are multiple sources of error:
The discrete mesh may not be an exact mesh for the polygon due to rounding errors (typically of the order of the machine $\varepsilon$). This gives slight perturbations for the mass and rigidity matrices.
The discrete solution comes from solving a linear system. This linear system is solved numerically, so there is an additional error here.
The difference between the analytical solution and the finite element one is usually quantified with a priori estimates depending on the mesh size $h$.
Usually only point 3. above is mentioned when dealing with error estimates from finite elements. I guess this is due to the fact that errors coming from points 1 and 2 above (rounding errors, linear systems) are usually orders of magnitude smaller than the discretization error in 3. However, I am interested in knowing more about how one can quantify the errors coming from the first two points and eventual references treating these aspects.
Can you indicate references in the literature or the main ideas that can be used in order to better understand errors coming from points 1-2 above?