NONCONFORMING FEMs FOR AN OPTIMAL DESIGN PROBLEM

摘要

Some optimal design problems in topology optimization eventually lead to a degenerate convex minimization problem E(v) := integral(Omega) W(del v)dx - integral(Omega) f v dx for v is an element of H-0(1)(Omega) with possibly multiple minimizers u, but with a unique stress sigma := DW(del u). This paper proposes the discrete Raviart-Thomas mixed finite element method (dRT-MFEM) and establishes its equivalence with the Crouzeix-Raviart nonconforming finite element method. The convergence analysis combines the a priori convergence rate of the conforming FEM with the efficient a posterior error control of MFEM. Numerical experiments provide empirical evidence that the proposed dRT-MFEM overcomes the reliability-efficiency gap for the first time.