Two-grid Method for Linear Elasticity on Unstructured Meshes

We propose an abstract two-grid algorithm with convergence independent of the coarse-space size. The abstract algorithm is applied to problems of three-dimensional linear elasticity discretized on unstructured meshes. With no regularity assumptions we prove uniform convergence with respect to coarse-space size, domain, essential boundary conditions, and jumps in Young modulus. Numerical experiments confirm the theory and show that the method works well even if some assumptions of the theory are violated.