Questions tagged [elliptic-pde]

What library can one use to compute efficiently the lowest eigenvalues of the Laplace operator in a polyhedral domain in $R^3$? For the application I have in mind one has to consider very acute polyhedra (which moreover are non-convex) so it would…

Wikipedia tells me that the equations for linear elasticity and biharmonic equations have the same solution for Dirichlet boundary condition. How do you show the equivalence in the variational formulation?

I'm looking for an explanation of why the jump $[\nabla u]=[u] =0$ assuming $u \in H^2(\Omega)$. We know that according to an embedding theorem, $H^1(\Omega)$ is a subspace of $C^0(\bar{\Omega})$ (space of continuous functions in $\bar{\Omega}$) so…