Patch‐smoother and multigrid for the dual formulation for linear elasticity

The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it based on stresses main unknowns. Thus quite attractive nearly incompressible and materials. Discretization with mixed finite elements will lead to—possibly large—linear saddle point systems. Whereas efficient multigrid methods exist solving problems plane elasticity materials, we propose a method that also stable limit. There are two challenges constructing elasticity. First, limit, matrix block related stress positive semidefinite. Second, belongs H div standard smoothers, working 1 regular problems, cannot be applied. We present novel patch-based smoother discuss different types of local boundary conditions patch subproblems. Based our patch-smoother, build solution resulting problem investigate its efficiency robustness. Numerical experiments show Dirichlet Robin work best eventually textbook performance.