(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
The p-Laplace problems in topology optimization eventually lead to a degenerate convex minimization problem E(v):= ∫_ΩW(∇v)dx − ∫_Ωf vdx for v∈W^1,p_0(Ω) with unique minimizer u and stress σ := DW(∇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 (CR-NCFEM). The sharper quasi-norm a priori and a posteriori error estimates of this two methods are presented. Numerical experiments are provided to verify the analysis.