Assuming a solid mechanics problem, linear elasticity, with a domain split in two by an interface that is not aligned with the mesh. The mesh is a quadtree with squares. There are different material properties at each side of the interface. Now we use AMR and the algorithm will refine the mesh along the boundary, but will never be able to align the mesh with the interface because of the quadtree. How will the stress converge for this case? Do the a priori error estimations still hold in the stresses near the interface?What if the interface was aligned with the mesh (making it jagged)?In this case we will have many re-entrant corners and I assume the stresses will not converge, but somehow, making the mesh finer and finer, that jagged interface will become somehow smoother. Is there any type of convergence possible here?Edit: I forgot to add that the method is finite element with linear quadrangular lagrange elements.
Convergence of the stress at an interface using AMR with quadtree meshes in a solid mechanics problem
pde;adaptive mesh refinement