Volume 10, Issue 6
Nonconforming FEMs for the p-Laplace Problem

D. J. Liu ,  A. Q. Li and Z. R. Chen

10.4208/aamm.OA-2018-0117

Adv. Appl. Math. Mech., 10 (2018), pp. 1365-1383.

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  • Abstract

The p-Laplace problems in topology optimization eventually lead to a degenerate convex minimization problem E(v):= ∫W(∇v)dx− ∫f vdx for v∈W1,p0(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.

  • History

Published online: 2018-09

  • AMS Subject Headings

65N12, 65N30, 65Y20

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