Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations the absence of exact rotational invariance space. An example is provided by membrane an orientational field, tuned to critical buckling point application in-plane stresses. Through detailed analysis, show that tr...

We study the approximation of spectrum least-squares operators arising from linear elasticity. consider a two-field (stress/displacement) and three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. prove priori estimates we confirm theoretical results simple two-dimensional numerical experiments.