Adaptive multigrid method using duality in plane elasticity

This work presents an adaptive multigrid method for the mixed formulation of plane elasticity problems. First, a mixed-hybrid formulation is introduced where the continuity of the normal components of the stress tensor is indirectly imposed using a Lagrange multiplier. Two di erent numerical approximations, naturally associated with the primal problem and the dual problem, are then proposed. The Complementary Energy Principle provides an a posteriori error estimate. For the e ective solving of both systems of equations, a non-standard multigrid algorithm has been designed that allows us to solve the two problems, dual and primal, with reasonable cost and in an integrated way. Finally, a signi cant numerical application is presented to check the e ciency of the error estimator and the good performance of the algorithm