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

D. J. Liu, A. Q. Li & Z. R. Chen

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

Published online: 2018-09

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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.

  • Keywords

Adaptive finite element methods nonconforming p-Laplace problem dual energy.

  • AMS Subject Headings

65N12 65N30 65Y20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-1365, author = {D. J. Liu, A. Q. Li and Z. R. Chen}, title = {Nonconforming FEMs for the p-Laplace Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {1365--1383}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0117}, url = {http://global-sci.org/intro/article_detail/aamm/12715.html} }
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