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A different perspective on the question is this: Newton's law says that mass times acceleration equals the sum of all forces. You are interested in the steady state case, so the acceleration is zero a …

The two descriptions you use describe different physical situations. In the first, you apply a given force (which you have assumed is normal to the surface, though it could of course also have a tang …

So so many places you have to rewrite. The whole mesh handling (accessing faces and edges from cells, neighbors from cells, ...). Shape functions. Dealing with the question of how the normal vector of …

You can't prescribe both Dirichlet and Neumann conditions, but you can prescribe a Robin-type boundary condition in which the normal stress (traction) is proportional to the displacement. You can thin …

You already know that at least theoretically, unconstrained matrices have a null space and consequently eigenvalues that are equal to zero. But, in practice, this is a meaningless condition because it …

All of the major finite element libraries (such as libMesh; FEniCS; or the project I run, deal.II) provide you with ready access to the system matrix and or any other matrices you need. They typically …

Your physical strain gauge gives you a single number, which means that it is represented by a functional $\varphi(\cdot)$ applied to the solution and its gradient (strain) everywhere. Let's say that i …

It is not true that the finite element solution is exact a nodes.

Nick Alger gives a nice explanation. Here is another one, possibly slightly simpler because it avoids the "should stay roughly the same" part. Let's say you want to compute the derivative of any matr …

The condition number for the stiffness matrix of any method (finite elements, finite volumes, finite differences) applied to a second order differential operator always grows as ${\cal O}(h^{-2})$ whe …

The finite element method is actually quite widely used in fluid flow problems, for example for the Stokes and Navier-Stokes equations. The delineation between the methods is more along the following …

$\vec\Phi = K_i \nabla u_i$ is the flux across the interface. For example, if $u$ is the thermal energy density and $K$ the thermal conductivity, then $\vec\Phi$ is the thermal energy flux. Energy con …

The truth is that I don't actually know very much about this, and so this may or may not be at all helpful. But let me sort my thoughts in the following way: Let's say for simplicity that you're tryin …