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Adaptive multigrid method using duality in plane elasticity
Author(s) -
Domínguez M del Carmen,
Ferragut Luis
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010110)50:1<95::aid-nme23>3.0.co;2-d
Subject(s) - multigrid method , lagrange multiplier , mathematical optimization , mathematics , estimator , a priori and a posteriori , duality (order theory) , elasticity (physics) , polygon mesh , partial differential equation , mathematical analysis , geometry , philosophy , statistics , materials science , epistemology , discrete mathematics , composite material
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 different 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 effective 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 significant numerical application is presented to check the efficiency of the error estimator and the good performance of the algorithm. Copyright © 2001 John Wiley & Sons, Ltd.